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Statistical Modeling of Modern Multivariate Data
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Statistical Modeling of Modern Multivariate Data

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (20 October 2023) | Viewed by 7687

Special Issue Editor

Prof. Dr. Anuradha Roy

E-Mail Website
Guest Editor
Department of Management Science and Statistics, The University of Texas at San Antonio, San Antonio, TX 78249, USA
Interests: multivariate analysis; multivariate repeated measures data; mixed-effects models; symbolic data analysis; Kronecker structured covariance matrix

Special Issue Information

Dear Colleagues,

We are pleased to announce the launch of a new Special Issue in Axioms, entitled “Statistical Modeling of Modern Multivariate Data”. Multivariate analysis plays a vital role in analyzing modern statistical data. Advances in computing power in the past few decades have greatly encouraged the collection of big and complex data in our everyday lives, across platforms. The recent development of a cheaper and more manageable way to store a large amount of digital data helps to register complex data endlessly in almost all fields of study, such as business, biology, ecology, and the environment, to name just a few. Complex data typically have datasets that are very large, high-dimensional, and/or have intricate structures. Traditional multivariate analysis frequently fails to analyze such data.

Often data do not follow multivariate normal distribution or have some outliers; thus, the data need to be modeled with skewed distribution or heavy tailed distribution. The purpose of this Special Issue is to explore new methodological and computational multivariate statistical models to analyze big, complex, high-dimensional, and structured data with symmetric or skewed distributions.

Prof. Dr. Anuradha Roy
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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • multivariate distributions
  • matrix-variate distributions
  • mixed effects models
  • longitudinal data analysis
  • Kronecker structured covariance matrix
  • correlated data
  • complex data
  • high-dimensional data
  • big data
  • data science methods
  • biomedical informatics
  • robustness
  • machine learning
  • statistical computing
  • pattern recognition
  • finite mixture models
  • non-normal errors

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Published Papers (4 papers)

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Research

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23 pages, 810 KiB  
Article
Exploring Dynamic Structures in Matrix-Valued Time Series via Principal Component Analysis
by Lynne Billard, Ahlame Douzal-Chouakria and S. Yaser Samadi
Axioms 2023, 12(6), 570; https://doi.org/10.3390/axioms12060570 - 8 Jun 2023
Cited by 6 | Viewed by 1621
Abstract
Time-series data are widespread and have inspired numerous research works in machine learning and data analysis fields for the classification and clustering of temporal data. While there are several clustering methods for univariate time series and a few for multivariate series, most methods [...] Read more.
Time-series data are widespread and have inspired numerous research works in machine learning and data analysis fields for the classification and clustering of temporal data. While there are several clustering methods for univariate time series and a few for multivariate series, most methods are based on distance and/or dissimilarity measures that do not fully utilize the time-dependency information inherent to time-series data. To highlight the main dynamic structure of a set of multivariate time series, this study extends the use of standard variance–covariance matrices in principal component analysis to cross-autocorrelation matrices at time lags k=1,2,…. This results in “principal component time series”. Simulations and a sign language dataset are used to demonstrate the effectiveness of the proposed method and its benefits in exploring the main structural features of multiple time series. Full article
(This article belongs to the Special Issue Statistical Modeling of Modern Multivariate Data)
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26 pages, 1010 KiB  
Article
Theoretical Validation of New Two-Dimensional One-Variable-Power Copulas
by Christophe Chesneau
Axioms 2023, 12(4), 392; https://doi.org/10.3390/axioms12040392 - 18 Apr 2023
Cited by 2 | Viewed by 1372
Abstract
One of the most effective ways to illustrate the relationship between two quantitative variables is to describe the corresponding two-dimensional copula. This approach is acknowledged as practical, nonredundant, and computationally manageable in the context of data analysis. Modern data, however, contain a wide [...] Read more.
One of the most effective ways to illustrate the relationship between two quantitative variables is to describe the corresponding two-dimensional copula. This approach is acknowledged as practical, nonredundant, and computationally manageable in the context of data analysis. Modern data, however, contain a wide variety of dependent structures, and the copulas now in use may not provide the best model for all of them. As a result, researchers seek to innovate by building novel copulas with appealing properties that are also based on original methodologies. The foundations are theoretical; for a copula to be validated, it must meet specific requirements, which frequently dictate the constraints that must be placed on the relevant parameters. In this article, we make a contribution to the understudied field of one-variable-power copulas. We first identify the specific assumptions that, in theory, validate copulas of such nature. Some other general copulas and inequalities are discussed. Our general results are illustrated with numerous examples depending on two or three parameters. We also prove that strong connections exist between our assumptions and well-established distributions. To highlight the importance of our findings, we emphasize a particular two-parameter, one-variable-power copula that unifies the definition of some other copulas. We reveal its versatile shapes, related functions, various symmetry, Archimedean nature, geometric invariance, copula ordering, quadrant dependence, tail dependence, correlations, and distribution generation. Numerical tables and graphics are produced to support some of these properties. The estimation of the parameters based on data is discussed. As a complementary contribution, two new, intriguing one-variable-power copulas beyond the considered general form are finally presented and studied. Full article
(This article belongs to the Special Issue Statistical Modeling of Modern Multivariate Data)
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17 pages, 4713 KiB  
Article
An Expectation-Maximization Algorithm for Combining a Sample of Partially Overlapping Covariance Matrices
by Deniz Akdemir, Mohamed Somo and Julio Isidro-Sanchéz
Axioms 2023, 12(2), 161; https://doi.org/10.3390/axioms12020161 - 4 Feb 2023
Cited by 1 | Viewed by 1508
Abstract
The generation of unprecedented amounts of data brings new challenges in data management, but also an opportunity to accelerate the identification of processes of multiple science disciplines. One of these challenges is the harmonization of high-dimensional unbalanced and heterogeneous data. In this manuscript, [...] Read more.
The generation of unprecedented amounts of data brings new challenges in data management, but also an opportunity to accelerate the identification of processes of multiple science disciplines. One of these challenges is the harmonization of high-dimensional unbalanced and heterogeneous data. In this manuscript, we propose a statistical approach to combine incomplete and partially-overlapping pieces of covariance matrices that come from independent experiments. We assume that the data are a random sample of partial covariance matrices sampled from Wishart distributions and we derive an expectation-maximization algorithm for parameter estimation. We demonstrate the properties of our method by (i) using simulation studies and (ii) using empirical datasets. In general, being able to make inferences about the covariance of variables not observed in the same experiment is a valuable tool for data analysis since covariance estimation is an important step in many statistical applications, such as multivariate analysis, principal component analysis, factor analysis, and structural equation modeling. Full article
(This article belongs to the Special Issue Statistical Modeling of Modern Multivariate Data)
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Other

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32 pages, 4078 KiB  
Tutorial
Multilevel Ordinal Logit Models: A Proportional Odds Application Using Data from Brazilian Higher Education Institutions
by Rafael de Freitas Souza, Fabiano Guasti Lima and Hamilton Luiz Corrêa
Axioms 2024, 13(1), 47; https://doi.org/10.3390/axioms13010047 - 12 Jan 2024
Cited by 1 | Viewed by 2149
Abstract
This tutorial delves into the application of proportional odds-type ordinal logistic regression to assess the impact of incorporating both fixed and random effects when predicting the rankings of Brazilian universities in a well-established international academic assessment utilizing authentic data. In addition to offering [...] Read more.
This tutorial delves into the application of proportional odds-type ordinal logistic regression to assess the impact of incorporating both fixed and random effects when predicting the rankings of Brazilian universities in a well-established international academic assessment utilizing authentic data. In addition to offering valuable insights into the estimation of ordinal logistic models, this study underscores the significance of integrating random effects into the analysis and addresses the potential pitfalls associated with the inappropriate treatment of phenomena exhibiting categorical ordinal characteristics. Furthermore, we have made the R language code and dataset available as supplementary resources for the replication. Full article
(This article belongs to the Special Issue Statistical Modeling of Modern Multivariate Data)
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