Research

24 pages, 1927 KiB

Open AccessArticle

Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model

by Rodrigo Puentes, Carolina Marchant, Víctor Leiva, Jorge I. Figueroa-Zúñiga and Fabrizio Ruggeri

Mathematics 2021, 9(6), 645; https://0-doi-org.brum.beds.ac.uk/10.3390/math9060645 - 18 Mar 2021

Cited by 12 | Viewed by 1850

Abstract

Improving air quality is an important environmental challenge of our time. Chile currently has one of the most stable and emerging economies in Latin America, where human impact on natural resources and air quality does not go unperceived. Santiago, the capital of Chile, [...] Read more.

Improving air quality is an important environmental challenge of our time. Chile currently has one of the most stable and emerging economies in Latin America, where human impact on natural resources and air quality does not go unperceived. Santiago, the capital of Chile, is one of the cities in which particulate matter (PM) levels exceed national and international limits. Its location and climate cause critical conditions for human health when interaction with anthropogenic emissions is present. In this paper, we propose a predictive model based on bivariate regression to estimate PM levels, related to PM2.5 and PM10, simultaneously. Birnbaum-Saunders distributions are used in the joint modeling of real-world PM2.5 and PM10 data by considering as covariates some relevant meteorological variables employed in similar studies. The Mahalanobis distance is utilized to assess bivariate outliers and to detect suitability of the distributional assumption. In addition, we use the local influence technique for analyzing the impact of a perturbation on the overall estimation of model parameters. In the predictions, we check the categorization for the observed and predicted cases of the model according to the primary air quality regulations for PM. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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22 pages, 453 KiB

Open AccessArticle

A New Algorithm for Computing Disjoint Orthogonal Components in the Three-Way Tucker Model

by Carlos Martin-Barreiro, John A. Ramirez-Figueroa, Ana B. Nieto-Librero, Víctor Leiva, Ana Martin-Casado and M. Purificación Galindo-Villardón

Mathematics 2021, 9(3), 203; https://0-doi-org.brum.beds.ac.uk/10.3390/math9030203 - 20 Jan 2021

Cited by 11 | Viewed by 2229

Abstract

One of the main drawbacks of the traditional methods for computing components in the three-way Tucker model is the complex structure of the final loading matrices preventing an easy interpretation of the obtained results. In this paper, we propose a heuristic algorithm for [...] Read more.

One of the main drawbacks of the traditional methods for computing components in the three-way Tucker model is the complex structure of the final loading matrices preventing an easy interpretation of the obtained results. In this paper, we propose a heuristic algorithm for computing disjoint orthogonal components facilitating the analysis of three-way data and the interpretation of results. We observe in the computational experiments carried out that our novel algorithm ameliorates this drawback, generating final loading matrices with a simple structure and then easier to interpret. Illustrations with real data are provided to show potential applications of the algorithm. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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11 pages, 514 KiB

Open AccessArticle

Sign, Wilcoxon and Mann-Whitney Tests for Functional Data: An Approach Based on Random Projections

by Rafael Meléndez, Ramón Giraldo and Víctor Leiva

Mathematics 2021, 9(1), 44; https://0-doi-org.brum.beds.ac.uk/10.3390/math9010044 - 28 Dec 2020

Cited by 14 | Viewed by 3288

Abstract

Sign, Wilcoxon and Mann-Whitney tests are nonparametric methods in one or two-sample problems. The nonparametric methods are alternatives used for testing hypothesis when the standard methods based on the Gaussianity assumption are not suitable to be applied. Recently, the functional data analysis (FDA) [...] Read more.

Sign, Wilcoxon and Mann-Whitney tests are nonparametric methods in one or two-sample problems. The nonparametric methods are alternatives used for testing hypothesis when the standard methods based on the Gaussianity assumption are not suitable to be applied. Recently, the functional data analysis (FDA) has gained relevance in statistical modeling. In FDA, each observation is a curve or function which usually is a realization of a stochastic process. In the literature of FDA, several methods have been proposed for testing hypothesis with samples coming from Gaussian processes. However, when this assumption is not realistic, it is necessary to utilize other approaches. Clustering and regression methods, among others, for non-Gaussian functional data have been proposed recently. In this paper, we propose extensions of the sign, Wilcoxon and Mann-Whitney tests to the functional data context as methods for testing hypothesis when we have one or two samples of non-Gaussian functional data. We use random projections to transform the functional problem into a scalar one, and then we proceed as in the standard case. Based on a simulation study, we show that the proposed tests have a good performance. We illustrate the methodology by applying it to a real data set. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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19 pages, 459 KiB

Open AccessArticle

Data-Influence Analytics in Predictive Models Applied to Asthma Disease

by Alejandra Tapia, Viviana Giampaoli, Víctor Leiva and Yuhlong Lio

Mathematics 2020, 8(9), 1587; https://0-doi-org.brum.beds.ac.uk/10.3390/math8091587 - 15 Sep 2020

Cited by 3 | Viewed by 2216

Abstract

Asthma is one of the most common chronic diseases around the world and represents a serious problem in human health. Predictive models have become important in medical sciences because they provide valuable information for data-driven decision-making. In this work, a methodology of data-influence [...] Read more.

Asthma is one of the most common chronic diseases around the world and represents a serious problem in human health. Predictive models have become important in medical sciences because they provide valuable information for data-driven decision-making. In this work, a methodology of data-influence analytics based on mixed-effects logistic regression models is proposed for detecting potentially influential observations which can affect the quality of these models. Global and local influence diagnostic techniques are used simultaneously in this detection, which are often used separately. In addition, predictive performance measures are considered for this analytics. A study with children and adolescent asthma real data, collected from a public hospital of São Paulo, Brazil, is conducted to illustrate the proposed methodology. The results show that the influence diagnostic methodology is helpful for obtaining an accurate predictive model that provides scientific evidence when data-driven medical decision-making. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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13 pages, 997 KiB

Open AccessArticle

Cokriging Prediction Using as Secondary Variable a Functional Random Field with Application in Environmental Pollution

by Ramón Giraldo, Luis Herrera and Víctor Leiva

Mathematics 2020, 8(8), 1305; https://0-doi-org.brum.beds.ac.uk/10.3390/math8081305 - 06 Aug 2020

Cited by 29 | Viewed by 3371

Abstract

Cokriging is a geostatistical technique that is used for spatial prediction when realizations of a random field are available. If a secondary variable is cross-correlated with the primary variable, both variables may be employed for prediction by means of cokriging. In this work, [...] Read more.

Cokriging is a geostatistical technique that is used for spatial prediction when realizations of a random field are available. If a secondary variable is cross-correlated with the primary variable, both variables may be employed for prediction by means of cokriging. In this work, we propose a predictive model that is based on cokriging when the secondary variable is functional. As in the ordinary cokriging, a co-regionalized linear model is needed in order to estimate the corresponding auto-correlations and cross-correlations. The proposed model is utilized for predicting the environmental pollution of particulate matter when considering wind speed curves as functional secondary variable. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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18 pages, 445 KiB

Open AccessEditor’s ChoiceArticle

Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers

by Henry Velasco, Henry Laniado, Mauricio Toro, Víctor Leiva and Yuhlong Lio

Mathematics 2020, 8(8), 1259; https://0-doi-org.brum.beds.ac.uk/10.3390/math8081259 - 01 Aug 2020

Cited by 18 | Viewed by 3528

Abstract

Both cell-wise and case-wise outliers may appear in a real data set at the same time. Few methods have been developed in order to deal with both types of outliers when formulating a regression model. In this work, a robust estimator is proposed [...] Read more.

Both cell-wise and case-wise outliers may appear in a real data set at the same time. Few methods have been developed in order to deal with both types of outliers when formulating a regression model. In this work, a robust estimator is proposed based on a three-step method named 3S-regression, which uses the comedian as a highly robust scatter estimate. An intensive simulation study is conducted in order to evaluate the performance of the proposed comedian 3S-regression estimator in the presence of cell-wise and case-wise outliers. In addition, a comparison of this estimator with recently developed robust methods is carried out. The proposed method is also extended to the model with continuous and dummy covariates. Finally, a real data set is analyzed for illustration in order to show potential applications. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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14 pages, 266 KiB

Open AccessArticle

Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions

by Lauren Sauer, Yuhlong Lio and Tzong-Ru Tsai

Mathematics 2020, 8(7), 1176; https://0-doi-org.brum.beds.ac.uk/10.3390/math8071176 - 17 Jul 2020

Cited by 10 | Viewed by 2181

Abstract

In this paper, the reliability of a k-component system, in which all components are subject to common stress, is considered. The multicomponent system will continue to survive if at least s out of k components’ strength exceed the common stress. The system [...] Read more.

In this paper, the reliability of a k-component system, in which all components are subject to common stress, is considered. The multicomponent system will continue to survive if at least s out of k components’ strength exceed the common stress. The system reliability is investigated by utilizing the maximum likelihood estimator based on progressively type II censored samples from generalized Pareto distributions. The confidence interval of the system reliability can be obtained by using asymptotic normality with Fisher information matrix or bootstrap method approximation. An intensive simulation study is conducted to evaluate the performance of maximum likelihood estimators of the model parameters and system reliability for a variety of cases. For the confidence interval of the system reliability, simulation results indicate the bootstrap method approximation outperforms over the asymptotic normality approximation in terms of coverage probability. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

17 pages, 1638 KiB

Open AccessEditor’s ChoiceArticle

Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data

by Luis Sánchez, Víctor Leiva, Manuel Galea and Helton Saulo

Mathematics 2020, 8(6), 1000; https://0-doi-org.brum.beds.ac.uk/10.3390/math8061000 - 18 Jun 2020

Cited by 32 | Viewed by 2865

Abstract

In the present paper, a novel spatial quantile regression model based on the Birnbaum–Saunders distribution is formulated. This distribution has been widely studied and applied in many fields. To formulate such a spatial model, a parameterization of the multivariate Birnbaum–Saunders distribution, where one [...] Read more.

In the present paper, a novel spatial quantile regression model based on the Birnbaum–Saunders distribution is formulated. This distribution has been widely studied and applied in many fields. To formulate such a spatial model, a parameterization of the multivariate Birnbaum–Saunders distribution, where one of its parameters is associated with the quantile of the respective marginal distribution, is established. The model parameters are estimated by the maximum likelihood method. Finally, a data set is applied for illustrating the formulated model. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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28 pages, 453 KiB

Open AccessArticle

A Study on the X ¯ and S Control Charts with Unequal Sample Sizes

by Chanseok Park and Min Wang

Mathematics 2020, 8(5), 698; https://0-doi-org.brum.beds.ac.uk/10.3390/math8050698 - 02 May 2020

Cited by 6 | Viewed by 2757

Abstract

The control charts based on

\bar{X}

and S are widely used to monitor the mean and variability of variables and can help quality engineers identify and investigate causes of the process variation. The usual requirement behind these control charts is that the [...] Read more.

The control charts based on

\bar{X}

and S are widely used to monitor the mean and variability of variables and can help quality engineers identify and investigate causes of the process variation. The usual requirement behind these control charts is that the sample sizes from the process are all equal, whereas this requirement may not be satisfied in practice due to missing observations, cost constraints, etc. To deal with this situation, several conventional methods were proposed. However, some methods based on weighted average approaches and an average sample size often result in degraded performance of the control charts because the adopted estimators are biased towards underestimating the true population parameters. These observations motivate us to investigate the existing methods with rigorous proofs and we provide a guideline to practitioners for the best selection to construct the

\bar{X}

and S control charts when the sample sizes are not equal. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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19 pages, 909 KiB

Open AccessArticle

Diagnostic Analytics for an Autoregressive Model under the Skew-Normal Distribution

by Yonghui Liu, Guohua Mao, Víctor Leiva, Shuangzhe Liu and Alejandra Tapia

Mathematics 2020, 8(5), 693; https://0-doi-org.brum.beds.ac.uk/10.3390/math8050693 - 02 May 2020

Cited by 20 | Viewed by 2843

Abstract

Autoregressive models have played an important role in time series. In this paper, an autoregressive model based on the skew-normal distribution is considered. The estimation of its parameters is carried out by using the expectation–maximization algorithm, whereas the diagnostic analytics are conducted by [...] Read more.

Autoregressive models have played an important role in time series. In this paper, an autoregressive model based on the skew-normal distribution is considered. The estimation of its parameters is carried out by using the expectation–maximization algorithm, whereas the diagnostic analytics are conducted by means of the local influence method. Normal curvatures for the model under four perturbation schemes are established. Simulation studies are conducted to evaluate the performance of the proposed procedure. In addition, an empirical example involving weekly financial return data are analyzed using the procedure with the proposed diagnostic analytics, which has improved the model fit. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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17 pages, 3465 KiB

Open AccessArticle

On the Smoothing of the Generalized Extreme Value Distribution Parameters Using Penalized Maximum Likelihood: A Case Study on UVB Radiation Maxima in the Mexico City Metropolitan Area

by Alejandro Ivan Aguirre-Salado, Carlos Arturo Aguirre-Salado, Ernesto Alvarado, Alicia Santiago-Santos and Guillermo Arturo Lancho-Romero

Mathematics 2020, 8(3), 329; https://0-doi-org.brum.beds.ac.uk/10.3390/math8030329 - 03 Mar 2020

Cited by 1 | Viewed by 2131

Abstract

This paper concerns the use and implementation of penalized maximum likelihood procedures to fitting smoothing functions of the generalized extreme value distribution parameters to analyze spatial extreme values of ultraviolet B (UVB) radiation across the Mexico City metropolitan area in the period 2000–2018. [...] Read more.

This paper concerns the use and implementation of penalized maximum likelihood procedures to fitting smoothing functions of the generalized extreme value distribution parameters to analyze spatial extreme values of ultraviolet B (UVB) radiation across the Mexico City metropolitan area in the period 2000–2018. The model was fitted using a flexible semi-parametric approach and the parameters were estimated by the penalized maximum likelihood (PML) method. In order to investigate the performance of the model as well as the estimation method in the analysis of complex nonlinear trends for UVB radiation maxima, a simulation study was conducted. The results of the simulation study showed that penalized maximum likelihood yields better regularization to the model than the maximum likelihood estimates. We estimated return levels of extreme UVB radiation events through a nonstationary extreme value model using measurements of ozone (O₃), nitrogen oxides (NO_x), particles of 10 μm or less in diameter (PM₁₀), carbon monoxide (CO), relative humidity (RH) and sulfur dioxide (SO₂). The deviance statistics indicated that the nonstationary generalized extreme value (GEV) model adjusted was statistically better compared to the stationary model. The estimated smoothing functions of the location parameter of the GEV distribution on the spatial plane for different periods of time reveal the existence of well-defined trends in the maxima. In the temporal plane, a presence of temporal cyclic components oscillating over a weak linear component with a negative slope is noticed, while in the spatial plane, a weak nonlinear local trend is present on a plane with a positive slope towards the west, covering the entire study area. An explicit spatial estimate of the 25-year return period revealed that the more extreme risk levels are located in the western region of the study area. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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23 pages, 1147 KiB

Open AccessArticle

Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution

by Hua Xin, Zhifang Liu, Yuhlong Lio and Tzong-Ru Tsai

Mathematics 2020, 8(2), 162; https://0-doi-org.brum.beds.ac.uk/10.3390/math8020162 - 23 Jan 2020

Cited by 6 | Viewed by 2568

Abstract

The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) [...] Read more.

The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) samples, which are obtained from the doubly truncated three-parameter BurrXII distribution. Because computational difficulty occurs for maximum likelihood estimation method, two Bayesian procedures are suggested to estimate model parameters and lifetime quantiles under the normal use condition. A Markov Chain Monte Carlo approach using the Metropolis–Hastings algorithm via Gibbs sampling is built to obtain Bayes estimators of the model parameters and to construct credible intervals. The proposed Bayesian estimation procedures are simple for practical use, and the obtained Bayes estimates are reliable for evaluating the reliability of lifetime products based on ALT samples. Monte Carlo simulations were conducted to evaluate the performance of these two Bayesian estimation procedures. Simulation results show that the second Bayesian estimation procedure outperforms the first Bayesian estimation procedure in terms of bias and mean squared error when users do not have sufficient knowledge to set up hyperparameters in the prior distributions. Finally, a numerical example about oil-well pumps is used for illustration. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation)

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