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Mathematics
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Advances of Functional and High-Dimensional Data Analysis
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Advances of Functional and High-Dimensional Data Analysis

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 6822

Special Issue Editor

Prof. Dr. Jin-Ting Zhang

E-Mail Website
Guest Editor
Department of Statistics and Applied Probability, National University of Singapore, Singapore, Singapore
Interests: statistical inferences on data in separate metric spaces; high-dimensional data analysis; functional data analysis; beherens-fisher problems for ANOVA and MANOVA; nonparametric mixed-effects modeling in longitudinal data analysis; nonparametric techniques in medical applications

Special Issue Information

Dear Colleagues,

Functional data are referred to as data whose observation units are functions (curves, surfaces, or anything else varying over a continuum), and high-dimensional data are referred to as data whose dimension or number of features is of comparable size or is larger than the number of observations.  With the development of modern data collection technology, functional and high-dimensional data are commonly seen and readily available in many research areas nowadays. They present a variety of new challenges because classical theories and methodologies can surprisingly fail to work. Therefore, in the past two decades, much attention has been paid to developing new theories and methodologies for analyzing functional and high-dimensional data.

In this Special Issue, we are interested in research papers concerned with theoretical, computational, or data analytic aspects of functional and high-dimensional data analysis. Papers in the following areas are particularly welcome:

  • Classification, clustering, and discrimination;
  • Data mining and machine learning techniques;
  • Dependent functional or high-dimensional data analysis;
  • Hypothesis testing about equality of mean, covariance operators, or distributions;
  • Parametric and nonparametric regression and prediction;
  • Other advances concerning functional or high-dimensional data analysis.

In order to be considered for publication, a paper should have developed some new theories or methodologies for analyzing functional or high-dimensional data. Quick publication is possible for interesting research work.

Prof. Dr. Jin-Ting Zhang
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Functional data
  • High-dimensional data
  • Data analytical techniques
  • Innovative theory and methodology

Published Papers (5 papers)

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Research

21 pages, 1490 KiB  
Article
Testing Equality of Several Distributions at High Dimensions: A Maximum-Mean-Discrepancy-Based Approach
by Zhi Peng Ong, Aixiang Andy Chen, Tianming Zhu and Jin-Ting Zhang
Mathematics 2023, 11(20), 4374; https://0-doi-org.brum.beds.ac.uk/10.3390/math11204374 - 21 Oct 2023
Viewed by 729
Abstract
With the development of modern data collection techniques, researchers often encounter high-dimensional data across various research fields. An important problem is to determine whether several groups of these high-dimensional data originate from the same population. To address this, this paper presents a novel [...] Read more.
With the development of modern data collection techniques, researchers often encounter high-dimensional data across various research fields. An important problem is to determine whether several groups of these high-dimensional data originate from the same population. To address this, this paper presents a novel k-sample test for equal distributions for high-dimensional data, utilizing the Maximum Mean Discrepancy (MMD). The test statistic is constructed using a V-statistic-based estimator of the squared MMD derived for several samples. The asymptotic null and alternative distributions of the test statistic are derived. To approximate the null distribution accurately, three simple methods are described. To evaluate the performance of the proposed test, two simulation studies and a real data example are presented, demonstrating the effectiveness and reliability of the test in practical applications. Full article
(This article belongs to the Special Issue Advances of Functional and High-Dimensional Data Analysis)
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22 pages, 1289 KiB  
Article
Minimum Residual Sum of Squares Estimation Method for High-Dimensional Partial Correlation Coefficient
by Jingying Yang, Guishu Bai and Mei Yan
Mathematics 2023, 11(20), 4311; https://0-doi-org.brum.beds.ac.uk/10.3390/math11204311 - 16 Oct 2023
Viewed by 855
Abstract
The partial correlation coefficient (Pcor) is a vital statistical tool employed across various scientific domains to decipher intricate relationships and reveal inherent mechanisms. However, existing methods for estimating Pcor often overlook its accurate calculation. In response, this paper introduces a minimum residual sum [...] Read more.
The partial correlation coefficient (Pcor) is a vital statistical tool employed across various scientific domains to decipher intricate relationships and reveal inherent mechanisms. However, existing methods for estimating Pcor often overlook its accurate calculation. In response, this paper introduces a minimum residual sum of squares Pcor estimation method (MRSS), a high-precision approach tailored for high-dimensional scenarios. Notably, the MRSS algorithm reduces the estimation bias encountered with positive Pcor. Through simulations on high-dimensional data, encompassing both sparse and non-sparse conditions, MRSS consistently mitigates the arithmetic bias for positive Pcors, surpassing other algorithms discussed. For instance, for large sample sizes (n≥100) with Pcor > 0, the MRSS algorithm reduces the MSE and RMSE by about 30–70% compared to other algorithms. The robustness and stability of the MRSS algorithm is demonstrated by the sensitivity analysis with variance and sparsity parameters. Stocks data in China’s A-share market are employed to showcase the MRSS methodology’s practicality. Full article
(This article belongs to the Special Issue Advances of Functional and High-Dimensional Data Analysis)
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28 pages, 3094 KiB  
Article
Optimal Estimation of Large Functional and Longitudinal Data by Using Functional Linear Mixed Model
by Mengfei Ran and Yihe Yang
Mathematics 2022, 10(22), 4322; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224322 - 17 Nov 2022
Cited by 1 | Viewed by 1371
Abstract
The estimation of large functional and longitudinal data, which refers to the estimation of mean function, estimation of covariance function, and prediction of individual trajectory, is one of the most challenging problems in the field of high-dimensional statistics. Functional Principal Components Analysis (FPCA) [...] Read more.
The estimation of large functional and longitudinal data, which refers to the estimation of mean function, estimation of covariance function, and prediction of individual trajectory, is one of the most challenging problems in the field of high-dimensional statistics. Functional Principal Components Analysis (FPCA) and Functional Linear Mixed Model (FLMM) are two major statistical tools used to address the estimation of large functional and longitudinal data; however, the former suffers from a dramatically increasing computational burden while the latter does not have clear asymptotic properties. In this paper, we propose a computationally effective estimator of large functional and longitudinal data within the framework of FLMM, in which all the parameters can be automatically estimated. Under certain regularity assumptions, we prove that the mean function estimation and individual trajectory prediction reach the minimax lower bounds of all nonparametric estimations. Through numerous simulations and real data analysis, we show that our new estimator outperforms the traditional FPCA in terms of mean function estimation, individual trajectory prediction, variance estimation, covariance function estimation, and computational effectiveness. Full article
(This article belongs to the Special Issue Advances of Functional and High-Dimensional Data Analysis)
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27 pages, 2419 KiB  
Article
Multiple Change-Point Detection in a Functional Sample via the 𝒢-Sum Process
by Tadas Danielius and Alfredas Račkauskas
Mathematics 2022, 10(13), 2294; https://0-doi-org.brum.beds.ac.uk/10.3390/math10132294 - 30 Jun 2022
Viewed by 1311
Abstract
We first define the G-CUSUM process and investigate its theoretical aspects including asymptotic behavior. By choosing different sets G, we propose some tests for multiple change-point detections in a functional sample. We apply the proposed testing procedures to the real-world neurophysiological [...] Read more.
We first define the G-CUSUM process and investigate its theoretical aspects including asymptotic behavior. By choosing different sets G, we propose some tests for multiple change-point detections in a functional sample. We apply the proposed testing procedures to the real-world neurophysiological data and demonstrate how it can identify the existence of the multiple change-points and localize them. Full article
(This article belongs to the Special Issue Advances of Functional and High-Dimensional Data Analysis)
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11 pages, 306 KiB  
Article
A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations
by Mohammad Arashi, Mina Norouzirad, Mahdi Roozbeh and Naushad Mamode Khan
Mathematics 2021, 9(23), 3057; https://0-doi-org.brum.beds.ac.uk/10.3390/math9233057 - 28 Nov 2021
Cited by 6 | Viewed by 1484
Abstract
The ridge regression estimator is a commonly used procedure to deal with multicollinear data. This paper proposes an estimation procedure for high-dimensional multicollinear data that can be alternatively used. This usage gives a continuous estimate, including the ridge estimator as a particular case. [...] Read more.
The ridge regression estimator is a commonly used procedure to deal with multicollinear data. This paper proposes an estimation procedure for high-dimensional multicollinear data that can be alternatively used. This usage gives a continuous estimate, including the ridge estimator as a particular case. We study its asymptotic performance for the growing dimension, i.e., p→∞ when n is fixed. Under some mild regularity conditions, we prove the proposed estimator’s consistency and derive its asymptotic properties. Some Monte Carlo simulation experiments are executed in their performance, and the implementation is considered to analyze a high-dimensional genetic dataset. Full article
(This article belongs to the Special Issue Advances of Functional and High-Dimensional Data Analysis)
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