Nonparametric Statistical Methods and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 29345

Special Issue Editor

Department of Economics & Management, University of Ferrara, 44121 Ferrara, Italy
Interests: multivariate analysis; nonparametric statistics; permutation tests; composite indicators

Special Issue Information

Dear Colleagues,

You are kindly invited to contribute to this Special Issue on “Nonparametric Statistical Methods and Their Applications” with an original research paper or a comprehensive review. The main focus is on new theoretical proposals, applications and/or computational aspects of nonparametric statistical methods. The papers should cover a wide spectrum of topics concerning nonparametric and semiparametric methods for inferential or exploratory data analysis. The methodological topics of interest include but are not limited to:

  • Rank tests
  • Permutation tests
  • Goodness-of-fit tests
  • Bootstrap methods
  • Nonparametric curve and/or density estimation
  • Regression smoothing
  • Symmetry testing
  • Robust estimation
  • Nonparametric filtering
  • Ranked set sampling
  • Bayesian nonparametrics
  • Semiparametric models and procedures

Many statistical methods are often based on assumptions that cannot be tested, are not plausible or are not justified by asymptotic theories (e.g., with small sample sizes). For these reasons, nonparametric statistical methods have become increasingly important and widespread in several empirical disciplines. A non-exhaustive list of the application-based areas of interest for the Special Issue is as follows: psychology, business and economics, finance, economic and social sciences, biomedical sciences, engineering, chemistry, environmental sciences, quality evaluation, multicriteria decision making, big data, DOE, computer science, computational intelligence, and machine learning.  

Prof. Dr. Stefano Bonnini
Guest Editor

Manuscript Submission Information

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Keywords

  • nonparametric statistics
  • semiparametric statistical methods
  • curve estimation
  • multivariate analysis
  • statistical algorithms and machine learning
  • resampling methods
  • distribution-free techniques

Published Papers (22 papers)

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Research

11 pages, 281 KiB  
Article
A Non-Parametric Sequential Procedure for the Generalized Partition Problem
by Tumulesh K. S. Solanky and Jie Zhou
Mathematics 2024, 12(4), 591; https://0-doi-org.brum.beds.ac.uk/10.3390/math12040591 - 17 Feb 2024
Viewed by 339
Abstract
In selection and ranking, the partitioning of treatments by comparing them to a control treatment is an important statistical problem. For over eighty years, this problem has been investigated by a number of researchers via various statistical designs to specify the partitioning criteria [...] Read more.
In selection and ranking, the partitioning of treatments by comparing them to a control treatment is an important statistical problem. For over eighty years, this problem has been investigated by a number of researchers via various statistical designs to specify the partitioning criteria and optimal strategies for data collection. Many researchers have proposed designs in order to generalize formulations known at that time. One such generalization adopted the indifference-zone formulation to designate the region between the boundaries for “good” and “bad” treatments as the indifference zone. Since then, this formulation has been adopted by a number of researchers to study various aspects of the partition problem. In this paper, a non-parametric purely sequential procedure is formulated for the partition problem. The “first-order” asymptotic properties of the proposed non-parametric procedure are derived. The performance of the proposed non-parametric procedure for small and moderate sample sizes is studied via Monte Carlo simulations. An example is provided to illustrate the proposed procedure. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
15 pages, 2836 KiB  
Article
Design and Analysis of Extended Exponentially Weighted Moving Average Signed-Rank Control Charts for Monitoring the Process Mean
by Khanittha Talordphop, Yupaporn Areepong and Saowanit Sukparungsee
Mathematics 2023, 11(21), 4482; https://0-doi-org.brum.beds.ac.uk/10.3390/math11214482 - 30 Oct 2023
Viewed by 693
Abstract
In the real world, a nonparametric control chart is a powerful substitute for enhancing outcome quality, although the fundamental procedure characteristic often fails to match the distribution assumptions. This study aims to construct and evaluate an extended exponentially weighted moving average control chart [...] Read more.
In the real world, a nonparametric control chart is a powerful substitute for enhancing outcome quality, although the fundamental procedure characteristic often fails to match the distribution assumptions. This study aims to construct and evaluate an extended exponentially weighted moving average control chart based on signed-rank statistics (EEWMA-SR) for recognizing changes in procedures. According to the study, the proposed chart proves more potent recognition of shifts in the process mean, predominantly small shifts, than the other control charts by the average run length in Monte Carlo simulation. Applying the proposed control chart to an actual dataset yielded events that corroborated the study discoveries. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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21 pages, 6192 KiB  
Article
Optimal Bandwidth Selection Methods with Application to Wind Speed Distribution
by Necla Gündüz and Şule Karakoç
Mathematics 2023, 11(21), 4478; https://0-doi-org.brum.beds.ac.uk/10.3390/math11214478 - 29 Oct 2023
Viewed by 950
Abstract
Accurate estimation of the unknown probability density functions of critical variables, such as wind speed—which plays a pivotal role in harnessing clean energy—is essential for various scientific and practical applications. This research conducts a comprehensive comparative analysis of seven distinct bandwidth calculation techniques [...] Read more.
Accurate estimation of the unknown probability density functions of critical variables, such as wind speed—which plays a pivotal role in harnessing clean energy—is essential for various scientific and practical applications. This research conducts a comprehensive comparative analysis of seven distinct bandwidth calculation techniques across various normal distributions, using simulation as the evaluation method in the context of Kernel Density Estimation (KDE). This analysis includes the calculation of the optimal bandwidth and assessment of the performance of these methods with respect to Mean Squared Error (MSE), bias, and the optimal bandwidth value. The findings reveal that among the various bandwidth methods evaluated, the Bandwidth bandwidth-based Cross-Validation (BCV), especially for small sample sizes, consistently provides the closest result to the optimal bandwidth across most of the applied normal distributions. These results provide valuable insights into the selection of optimal bandwidths for accurate and reliable density estimation in the context of normal distributions. Another key aspect of this work is the extension of these methods to wind speed data in a specific region. Monthly wind speed kernel density estimates obtained using all seven bandwidth selection techniques show that Smoothed Cross-Validation (SCV) is suited for this type of real-world data. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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18 pages, 290 KiB  
Article
Treatment Benefit and Treatment Harm Rates with Nonignorable Missing Covariate, Endpoint, or Treatment
by Yi He, Linzhi Zheng and Peng Luo
Mathematics 2023, 11(21), 4459; https://0-doi-org.brum.beds.ac.uk/10.3390/math11214459 - 27 Oct 2023
Viewed by 490
Abstract
The average treatment effect is an important concept in causal inference. However, it fails to capture variation in response to treatment due to heterogeneity at many levels among patients in the target population. To study the heterogeneity in the treatment effect, researchers proposed [...] Read more.
The average treatment effect is an important concept in causal inference. However, it fails to capture variation in response to treatment due to heterogeneity at many levels among patients in the target population. To study the heterogeneity in the treatment effect, researchers proposed the concepts of treatment benefit rate (TBR) and treatment harm rate (THR). Howerver, in practice, missing data often occurs in treatment, endpoints, and covariates. In these cases, the conditions given by them are not enough to identify treatment benefit rate. In this article, we address the problem of identifying the treatment benefit rate and treatment harm rate when treatment or endpoints or covariates are missing. Different types of missing data mechanisms are assumed, including several situations of nonignorable missingness. We prove that the treatment benefit rate and treatment harm rate are identifiable under very mild conditions, and then construct estimators based on methods of the EM algorithm. The performance of the proposed inference procedure is evaluated via simulation studies. Lastly, we illustrate our method by real data sets. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
22 pages, 696 KiB  
Article
Nonparametric Estimation of Multivariate Copula Using Empirical Bayes Methods
by Lu Lu and Sujit Ghosh
Mathematics 2023, 11(20), 4383; https://0-doi-org.brum.beds.ac.uk/10.3390/math11204383 - 21 Oct 2023
Viewed by 979
Abstract
In the fields of finance, insurance, system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are easy to estimate but can be highly biased [...] Read more.
In the fields of finance, insurance, system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are easy to estimate but can be highly biased when such assumptions are false, while the empirical copulas are nonsmooth and often not genuine copulas, making the inference about dependence challenging in practice. As a compromise, the empirical Bernstein copula provides a smooth estimator, but the estimation of tuning parameters remains elusive. The proposed empirical checkerboard copula within a hierarchical empirical Bayes model alleviates the aforementioned issues and provides a smooth estimator based on multivariate Bernstein polynomials that itself is shown to be a genuine copula. Additionally, the proposed copula estimator is shown to provide a more accurate estimate of several multivariate dependence measures. Both theoretical asymptotic properties and finite-sample performances of the proposed estimator based on simulated data are presented and compared with some nonparametric estimators. An application to portfolio risk management is included based on stock prices data. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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17 pages, 641 KiB  
Article
Non-Parametric Test for Decreasing Uncertainty of Residual Life Distribution (DURL)
by Hassina Benaoudia and Amar Aissani
Mathematics 2023, 11(20), 4227; https://0-doi-org.brum.beds.ac.uk/10.3390/math11204227 - 10 Oct 2023
Viewed by 667
Abstract
In this paper, we propose a new statistic to test the monotonicity of uncertainty based on derivative criteria and the histogram method. We test the null hypothesis that residual entropy is constant against the fact that it decreases over time. Hence, by the [...] Read more.
In this paper, we propose a new statistic to test the monotonicity of uncertainty based on derivative criteria and the histogram method. We test the null hypothesis that residual entropy is constant against the fact that it decreases over time. Hence, by the fact that the exponential distribution is the distribution with a constant uncertainty, we establish the test exponential distribution against the decreasing uncertainty of residual life distribution. Consistency and asymptotic normality are proved. The critical values of the statistics are given by means of the Monte Carlo simulation method to decide on the test. Then, the power estimates of the new test are compared to those of the test based on the criteria of monotonicity of residual entropy. Finally, we show, with real survival data, that the distributions belong to a decreasing uncertainty residual life class. Moreover, by applying a test of goodness of fit, we confirm that the data follow parametric distributions belonging to a decreasing uncertainty of residual life class. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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21 pages, 644 KiB  
Article
On the Reliability of Machine Learning Models for Survival Analysis When Cure Is a Possibility
by Ana Ezquerro, Brais Cancela and Ana López-Cheda
Mathematics 2023, 11(19), 4150; https://0-doi-org.brum.beds.ac.uk/10.3390/math11194150 - 02 Oct 2023
Viewed by 1012
Abstract
In classical survival analysis, it is assumed that all the individuals will experience the event of interest. However, if there is a proportion of subjects who will never experience the event, then a standard survival approach is not appropriate, and cure models should [...] Read more.
In classical survival analysis, it is assumed that all the individuals will experience the event of interest. However, if there is a proportion of subjects who will never experience the event, then a standard survival approach is not appropriate, and cure models should be considered instead. This paper deals with the problem of adapting a machine learning approach for classical survival analysis to a situation when cure (i.e., not suffering the event) is a possibility. Specifically, a brief review of cure models and recent machine learning methodologies is presented, and an adaptation of machine learning approaches to account for cured individuals is introduced. In order to validate the proposed methods, we present an extensive simulation study in which we compare the performance of the adapted machine learning algorithms with existing cure models. The results show the good behavior of the semiparametric or the nonparametric approaches, depending on the simulated scenario. The practical utility of the methodology is showcased through two real-world dataset illustrations. In the first one, the results show the gain of using the nonparametric mixture cure model approach. In the second example, the results show the poor performance of some machine learning methods for small sample sizes. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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19 pages, 613 KiB  
Article
Optimal Grouping of Dependent Components in Parallel-Series and Series-Parallel Systems with Independent Subsystems Equipped with Starting Devices
by Narayanaswamy Balakrishnan, Ghobad Saadat Kia (Barmalzan), Aliakbar Hosseinzadeh and Mostafa Sattari
Mathematics 2023, 11(17), 3718; https://0-doi-org.brum.beds.ac.uk/10.3390/math11173718 - 29 Aug 2023
Viewed by 600
Abstract
In this paper, we consider parallel-series and series-parallel systems comprising dependent components that are drawn from a heterogeneous population consisting of m different subpopulations, and each subsystem is equipped with a starter device. We also make the assumption that the components within each [...] Read more.
In this paper, we consider parallel-series and series-parallel systems comprising dependent components that are drawn from a heterogeneous population consisting of m different subpopulations, and each subsystem is equipped with a starter device. We also make the assumption that the components within each subpopulation are dependent, while the subsystems themselves are independent. The joint distribution of these subsystems is modeled using an Archimedean copula. Our research considers a general setting in which each subpopulation has a different Archimedean copula for its dependence. By adopting this general setup, we investigate the stochastic, hazard rate, and reversed hazard rate orders between these systems. Furthermore, we provide several numerical examples to demonstrate all the theoretical results established in this study. These results broaden the scope of the known results in the existing literature. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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13 pages, 312 KiB  
Article
Quantile Regression Based on the Weighted Approach with Dependent Truncated Data
by Jin-Jian Hsieh and Cheng-Chih Hsieh
Mathematics 2023, 11(17), 3669; https://0-doi-org.brum.beds.ac.uk/10.3390/math11173669 - 25 Aug 2023
Viewed by 462
Abstract
This paper discusses the estimation of parameters in the quantile regression model for dependent truncated data. To account for the dependence between the survival time and the truncated time, the Archimedean copula model is used to construct the association. The parameters of the [...] Read more.
This paper discusses the estimation of parameters in the quantile regression model for dependent truncated data. To account for the dependence between the survival time and the truncated time, the Archimedean copula model is used to construct the association. The parameters of the Archimedean copula model are estimated using certain existing approaches. An inference procedure based on a weighted approach is proposed, where the weights are set according to the variables of interest in the quantile regression model. The finite sample performance of the proposed approach is examined through simulations, and the method is applied to analyze two real datasets: the transfusion-related AIDS dataset and the retirement community center dataset. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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14 pages, 303 KiB  
Article
An Approach to Integrating a Non-Probability Sample in the Population Census
by Ieva Burakauskaitė and Andrius Čiginas
Mathematics 2023, 11(8), 1782; https://0-doi-org.brum.beds.ac.uk/10.3390/math11081782 - 08 Apr 2023
Cited by 2 | Viewed by 1529
Abstract
Population censuses are increasingly using administrative information and sampling as alternatives to collecting detailed data from individuals. Non-probability samples can also be an additional, relatively inexpensive data source, although they require special treatment. In this paper, we consider methods for integrating a non-representative [...] Read more.
Population censuses are increasingly using administrative information and sampling as alternatives to collecting detailed data from individuals. Non-probability samples can also be an additional, relatively inexpensive data source, although they require special treatment. In this paper, we consider methods for integrating a non-representative volunteer sample into a population census survey, where the complementary probability sample is drawn from the rest of the population. We investigate two approaches to correcting non-probability sample selection bias: adjustment using propensity scores, which models participation in the voluntary sample, and doubly robust estimation, which has the property of persisting possible misspecification of the latter model. We combine the estimators of population parameters that correct the selection bias with the estimators based on a representative union of both samples. Our analysis shows that the availability of detailed auxiliary information simplifies the applied estimation procedures, which are efficient in the Lithuanian census survey. Our findings also reveal the biased nature of the non-probability sample. For instance, when estimating the proportions of professed religions, smaller religious communities exhibit a higher participation rate than other groups. The combination of estimators corrects such selection bias. Our methodology for combining the voluntary and probability samples can be applied to other sample surveys. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
24 pages, 786 KiB  
Article
Estimation of Fixed Effects Partially Linear Varying Coefficient Panel Data Regression Model with Nonseparable Space-Time Filters
by Bogui Li, Jianbao Chen and Shuangshuang Li
Mathematics 2023, 11(6), 1531; https://0-doi-org.brum.beds.ac.uk/10.3390/math11061531 - 21 Mar 2023
Cited by 1 | Viewed by 1100
Abstract
Space-time panel data widely exist in many research fields such as economics, management, geography and environmental science. It is of interest to study the relationship between response variable and regressors which come from above fields by establishing regression models. This paper introduces a [...] Read more.
Space-time panel data widely exist in many research fields such as economics, management, geography and environmental science. It is of interest to study the relationship between response variable and regressors which come from above fields by establishing regression models. This paper introduces a new fixed effects partially linear varying coefficient panel data regression model with nonseparable space-time filters. On the basis of approximating the varying coefficient functions with a powerful B-spline method, the profile quasi-maximum likelihood estimators of parameters and varying coefficient functions are constructed. Under some regular conditions, we derive their consistency and asymptotic normality. Monte Carlo simulation shows that our estimates have good finite performance and ignoring spatial and serial correlations may lead to inefficiency of estimates. Finally, the driving forces of Chinese resident consumption rate are studied using our estimation method. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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19 pages, 485 KiB  
Article
Exact Permutation and Bootstrap Distribution of Generalized Pairwise Comparisons Statistics
by William N. Anderson and Johan Verbeeck
Mathematics 2023, 11(6), 1502; https://0-doi-org.brum.beds.ac.uk/10.3390/math11061502 - 20 Mar 2023
Cited by 3 | Viewed by 1448
Abstract
To analyze multivariate outcomes in clinical trials, several authors have suggested generalizations of the univariate Mann–Whitney test. As the Mann–Whitney statistic compares the subjects’ outcome pairwise, the multivariate generalizations are known as generalized pairwise comparisons (GPC) statistics. For GPC statistics such as the [...] Read more.
To analyze multivariate outcomes in clinical trials, several authors have suggested generalizations of the univariate Mann–Whitney test. As the Mann–Whitney statistic compares the subjects’ outcome pairwise, the multivariate generalizations are known as generalized pairwise comparisons (GPC) statistics. For GPC statistics such as the net treatment benefit, the win ratio, and the win odds, asymptotic based or re-sampling tests have been suggested in the literature. However, asymptotic methods require a sufficiently high sample size to be accurate, and re-sampling methods come with a high computational burden. We use graph theory notation to obtain closed-form formulas for the expectation and the variance of the permutation and bootstrap sampling distribution of the GPC statistics, which can be utilized to develop fast and accurate inferential tests for each of the GPC statistics. A simple example and a simulation study demonstrate the accuracy of the exact permutation and bootstrap methods, even in very small samples. As the time complexity is O(N2), where N is the total number of patients, the exact methods are fast. In situations where asymptotic methods have been used to obtain these variance matrices, the new methods will be more accurate and equally fast. In situations where bootstrap has been used, the new methods will be both more accurate and much faster. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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13 pages, 8254 KiB  
Article
COVID-19 Data Analysis Using Bayesian Models and Nonparametric Geostatistical Models
by Mayer Alvo and Jingrui Mu
Mathematics 2023, 11(6), 1359; https://0-doi-org.brum.beds.ac.uk/10.3390/math11061359 - 10 Mar 2023
Cited by 3 | Viewed by 961
Abstract
Since December 2019, many statistical spatial–temporal methods have been developed to track and predict the spread of the COVID-19 pandemic. In this paper, we analyzed the COVID-19 dataset which includes the number of biweekly infected cases registered in Ontario from March 2020 to [...] Read more.
Since December 2019, many statistical spatial–temporal methods have been developed to track and predict the spread of the COVID-19 pandemic. In this paper, we analyzed the COVID-19 dataset which includes the number of biweekly infected cases registered in Ontario from March 2020 to the end of June 2021. We made use of Bayesian Spatial–temporal models and Area-to-point (ATP) and Area-to-area (ATA) Poisson Kriging models. With the Bayesian models, spatial–temporal effects and government intervention effects on infection risk are considered while the ATP Poisson Kriging models are used to display the spread of the pandemic over space. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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20 pages, 592 KiB  
Article
A Blockwise Empirical Likelihood Test for Gaussianity in Stationary Autoregressive Processes
by Chioneso S. Marange, Yongsong Qin, Raymond T. Chiruka and Jesca M. Batidzirai
Mathematics 2023, 11(4), 1041; https://0-doi-org.brum.beds.ac.uk/10.3390/math11041041 - 18 Feb 2023
Viewed by 907
Abstract
A new and simple blockwise empirical likelihood moment-based procedure to test if a stationary autoregressive process is Gaussian has been proposed. The proposed test utilizes the skewness and kurtosis moment constraints to develop the test statistic. The test nonparametrically accommodates the dependence in [...] Read more.
A new and simple blockwise empirical likelihood moment-based procedure to test if a stationary autoregressive process is Gaussian has been proposed. The proposed test utilizes the skewness and kurtosis moment constraints to develop the test statistic. The test nonparametrically accommodates the dependence in the time series data whilst exhibiting some useful properties of empirical likelihood, such as the Wilks theorem with the test statistic having a chi-square limiting distribution. A Monte Carlo simulation study shows that our proposed test has good control of type I error. The finite sample performance of the proposed test is evaluated and compared to some selected competitor tests for different sample sizes and a variety of alternative applied distributions by means of a Monte Carlo study. The results reveal that our proposed test is on average superior under the log-normal and chi-square alternatives for small to large sample sizes. Some real data studies further revealed the applicability and robustness of our proposed test in practice. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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13 pages, 1173 KiB  
Article
Public Debt, Governance, and Growth in Developing Countries: An Application of Quantile via Moments
by Kazi Musa, Kazi Sohag, Jamaliah Said, Farha Ghapar and Norli Ali
Mathematics 2023, 11(3), 650; https://0-doi-org.brum.beds.ac.uk/10.3390/math11030650 - 27 Jan 2023
Cited by 4 | Viewed by 4266
Abstract
Developing countries often encounter budget deficits by taking loans from internal and external sources. The effectiveness of public debt has been a long debate in the seminal and empirical literature. In this study, we investigate the effectiveness of public debt on economic growth, [...] Read more.
Developing countries often encounter budget deficits by taking loans from internal and external sources. The effectiveness of public debt has been a long debate in the seminal and empirical literature. In this study, we investigate the effectiveness of public debt on economic growth, incorporating the role of governance in 44 developing countries. In doing so, we applied the Quantile Via Moments approach to analyze heterogeneous panel data ranging 1990–2000 considering the scale and location properties under different economic circumstances. Our results show that public debt impedes economic growth in all quantiles. Our empirical finding corroborates our proposition that in the presence of good governance, public debt promotes economic growth in the medium to higher quantiles. The empirical findings of this study confirm that governance is far more important in promoting economic growth. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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16 pages, 329 KiB  
Article
On the Robustness and Sensitivity of Several Nonparametric Estimators via the Influence Curve Measure: A Brief Study
by Indranil Ghosh and Kathleen Fleming
Mathematics 2022, 10(17), 3100; https://0-doi-org.brum.beds.ac.uk/10.3390/math10173100 - 29 Aug 2022
Cited by 2 | Viewed by 1081
Abstract
The use of influence curve as a measure of sensitivity is not new in the literature but has not been properly explored to the best of our knowledge. In particular, the mathematical derivation of the influence function for several popular nonparametric estimators (such [...] Read more.
The use of influence curve as a measure of sensitivity is not new in the literature but has not been properly explored to the best of our knowledge. In particular, the mathematical derivation of the influence function for several popular nonparametric estimators (such as trimmed mean, α-winsorized mean, Pearson product moment correlation coefficient etc. among notable ones) is not given in adequate detail. Moreover, the summary of the final expressions given in some sporadic cases does not appear to be correct. In this article, we aim to examine and summarize the derivation of the influence curve for various well-known estimators for estimating the location of a population, many of which are considered in the nonparametric paradigm. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
20 pages, 562 KiB  
Article
Impact of COVID-19-Related Lockdown Measures on Economic and Social Outcomes in Lithuania
by Jurgita Markevičiūtė, Jolita Bernatavičienė, Rūta Levulienė, Viktor Medvedev, Povilas Treigys and Julius Venskus
Mathematics 2022, 10(15), 2734; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152734 - 02 Aug 2022
Cited by 2 | Viewed by 1902
Abstract
The current world crisis caused by the COVID-19 pandemic has transformed into an economic crisis, becoming a problem and a challenge not only for individual national economies but also for the world economy as a whole. The first global lockdown, which started in [...] Read more.
The current world crisis caused by the COVID-19 pandemic has transformed into an economic crisis, becoming a problem and a challenge not only for individual national economies but also for the world economy as a whole. The first global lockdown, which started in mid-March of 2020 and lasted for three months in Lithuania, affected the movement and behavior of the population, and had an impact on the economy. This research presents results on the impact of lockdown measures on the economy using nonparametric methods in combination with parametric ones. The impact on unemployment and salary inequality was estimated. To assess the impact of lockdown on the labor market, the analysis of the dynamics of the unemployment rate was performed using the results of the cluster analysis. The Lithuanian data were analyzed in the context of other countries, where the dynamics of the spread of the virus were similar. The salary inequality was measured by the Gini coefficient and analyzed using change point analysis, functional data analysis and linear regression. The study found that the greatest impact of the closure restrictions on socio-economic indicators was recorded in 2020, with a lower impact in 2021. The proposed multi-step approach could be applied to other countries and to various types of shocks and interventions, not only the COVID-19 crisis, in order to avoid adverse economic and social outcomes. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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13 pages, 772 KiB  
Article
Signature-Based Analysis of the Weighted-r-within-Consecutive-k-out-of-n: F Systems
by Ioannis S. Triantafyllou
Mathematics 2022, 10(15), 2554; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152554 - 22 Jul 2022
Cited by 3 | Viewed by 927
Abstract
In the present paper, we deliver a reliability study of the weighted-r-consecutive-k-out-of-n: F reliability systems consisting of independent and identically distributed components. The signature vector of the structures is arithmetically determined by the aid of an appropriate [...] Read more.
In the present paper, we deliver a reliability study of the weighted-r-consecutive-k-out-of-n: F reliability systems consisting of independent and identically distributed components. The signature vector of the structures is arithmetically determined by the aid of an appropriate Monte-Carlo simulation scheme. Several conclusions for the corresponding reliability polynomials are also drawn. An extensive numerical investigation is carried out to evaluate the performance of the weighted-r-consecutive-k-out-of-n: F reliability systems. Some stochastic signature-based comparisons among several members of the underlying family of reliability structures are also discussed. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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18 pages, 617 KiB  
Article
A Semiparametric Approach to Test for the Presence of INAR: Simulations and Empirical Applications
by Lucio Palazzo and Riccardo Ievoli
Mathematics 2022, 10(14), 2501; https://0-doi-org.brum.beds.ac.uk/10.3390/math10142501 - 18 Jul 2022
Viewed by 1081
Abstract
The present paper explores the application of bootstrap methods in testing for serial dependence in observed driven Integer-AutoRegressive (models) considering Poisson arrivals (P-INAR). To this end, a new semiparametric and restricted bootstrap algorithm is developed to ameliorate the performance of the score-based test [...] Read more.
The present paper explores the application of bootstrap methods in testing for serial dependence in observed driven Integer-AutoRegressive (models) considering Poisson arrivals (P-INAR). To this end, a new semiparametric and restricted bootstrap algorithm is developed to ameliorate the performance of the score-based test statistic, especially when the time series present small or moderately small lengths. The performance of the proposed bootstrap test, in terms of empirical size and power, is investigated through a simulation study even considering deviation from Poisson assumptions for innovations, i.e., overdispersion and underdispersion. Under non-Poisson innovations, the semiparametric bootstrap seems to “restore” inference, while the asymptotic test usually fails. Finally, the usefulness of this approach is shown via three empirical applications. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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15 pages, 640 KiB  
Article
Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models
by Xingcai Zhou, Guang Yang and Yu Xiang
Mathematics 2022, 10(13), 2321; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132321 - 02 Jul 2022
Viewed by 1368
Abstract
The paper considers quantile-wavelet estimation for time-varying coefficients by embedding a wavelet kernel into quantile regression. Our methodology is quite general in the sense that we do not require the unknown time-varying coefficients to be smooth curves of a common degree or the [...] Read more.
The paper considers quantile-wavelet estimation for time-varying coefficients by embedding a wavelet kernel into quantile regression. Our methodology is quite general in the sense that we do not require the unknown time-varying coefficients to be smooth curves of a common degree or the errors to be independently distributed. Quantile-wavelet estimation is robust to outliers or heavy-tailed data. The model is a dynamic time-varying model of nonlinear time series. A strong Bahadur order O2mn3/4(logn)1/2 for the estimation is obtained under mild conditions. As applications, the rate of uniform strong convergence and the asymptotic normality are derived. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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21 pages, 369 KiB  
Article
A Nonparametric Approach for Testing Long Memory in Stock Returns’ Higher Moments
by Massimiliano Giacalone and Demetrio Panarello
Mathematics 2022, 10(5), 707; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050707 - 24 Feb 2022
Cited by 1 | Viewed by 1570
Abstract
In this paper, by considering a model-based approach for conditional moment estimation, a nonparametric test was performed to study the long-memory property of higher moments. We considered the daily returns of the stocks included in the S&P500 index in the last ten years [...] Read more.
In this paper, by considering a model-based approach for conditional moment estimation, a nonparametric test was performed to study the long-memory property of higher moments. We considered the daily returns of the stocks included in the S&P500 index in the last ten years (for the period running from the 1st of January 2011 to the 1st of January 2021). We found that mean and skewness were characterized by short memory, while variance and shape had long memory. These results have deep implications in terms of asset allocation, option pricing and market efficiency evaluation. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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18 pages, 354 KiB  
Article
On Testing the Adequacy of the Inverse Gaussian Distribution
by James S. Allison, Steffen Betsch, Bruno Ebner and Jaco Visagie
Mathematics 2022, 10(3), 350; https://0-doi-org.brum.beds.ac.uk/10.3390/math10030350 - 24 Jan 2022
Cited by 4 | Viewed by 2011
Abstract
We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution based on a characterization of the cumulative distribution function (CDF). The new tests are of weighted L2-type depending on a tuning parameter. We develop the asymptotic theory under [...] Read more.
We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution based on a characterization of the cumulative distribution function (CDF). The new tests are of weighted L2-type depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a broad class of alternative distributions. These results guarantee that the parametric bootstrap procedure, which we employ to implement the test, is asymptotically valid and that the whole test procedure is consistent. A comparative simulation study for finite sample sizes shows that the new procedure is competitive to classical and recent tests, outperforming these other methods almost uniformly over a large set of alternative distributions. The use of the newly proposed test is illustrated with two observed data sets. Full article
(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)
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