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Symmetry
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Symmetry and Asymmetry in Multivariate Statistics and Data Science, Second...
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Symmetry and Asymmetry in Multivariate Statistics and Data Science, Second Edition

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 2103

Special Issue Editor

Dr. Nicola Maria Rinaldo Loperfido

E-Mail Website
Guest Editor
Dipartimento di Economia, Società e Politica, Università degli Studi di Urbino “Carlo Bo”, Via Saffi 42, 61029 Urbino, Italy
Interests: statistics; probability; linear algebra
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Due to the great success of our Special Issue "Symmetry and Asymmetry in Multivariate Statistics and Data Science" we decided to set up a second volume.

Symmetry plays a fundamental role in both probability and statistics. In probability theory, the main measures of location, that is, the mean and the median, coincide if the underlying distribution is symmetric. In statistical inference, the sample mean and the sample variance are uncorrelated when the sampled distribution is symmetric. Multivariate symmetry and asymmetry pose several challenging research problems, which are of interest in their own right as well as for their practical implications. How do departures from multivariate symmetry affect well-known statistical methods, such as, for example, multivariate regression, robust statistical inference, and tests on mean vectors? Does skewness help in recovering data features such as outliers, clusters, and nonlinearity? How can we accurately measure, parsimoniously model, and efficiently test departures from multivariate symmetry? Which mathematical tools are best suited to deal with multivariate skewness and with the third-order moments that are often used to assess it? All these problems have been investigated in different research fields, with researchers in one field being apparently oblivious to the results obtained in other fields. This Special Issue aims at providing a unified perspective on multivariate symmetry and asymmetry by means of theoretical results, informed reviews, simulation experiments, data examples, and computational methods.

Welcome to read the publications in "Symmetry and Asymmetry in Multivariate Statistics and Data Science" at https://www.mdpi.com/journal/symmetry/special_issues/Multivariate_Statistics_Data.

Dr. Nicola Maria Rinaldo Loperfido
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. Symmetry 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

  • asymmetry
  • cumulants
  • moments
  • multilinear algebra
  • skewness
  • symmetry
  • tensor

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Related Special Issue

Published Papers (2 papers)

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Research

29 pages, 1206 KiB  
Article
Model Error Modeling for a Class of Multivariable Systems Utilizing Stochastic Embedding Approach with Gaussian Mixture Models
by Rafael Orellana, Maria Coronel, Rodrigo Carvajal, Pedro Escárate and Juan C. Agüero
Symmetry 2025, 17(3), 426; https://doi.org/10.3390/sym17030426 - 12 Mar 2025
Viewed by 400
Abstract
Many real-world multivariable systems need to be modeled to capture the interconnected behavior of their physical variables and to understand how uncertainty in actuators and sensors affects the system dynamics. In system identification, some estimation algorithms are formulated as multivariate data problems by [...] Read more.
Many real-world multivariable systems need to be modeled to capture the interconnected behavior of their physical variables and to understand how uncertainty in actuators and sensors affects the system dynamics. In system identification, some estimation algorithms are formulated as multivariate data problems by assuming symmetric noise distributions, yielding deterministic system models. Nevertheless, modern multivariable systems must incorporate the uncertainty behavior as a part of the system model structure, taking advantage of asymmetric distributions to model the uncertainty. This paper addresses the uncertainty modeling and identification of a class of multivariable linear dynamic systems, adopting a Stochastic Embedding approach. We consider a nominal system model and a Gaussian mixture distributed error-model driven by an exogenous input signal. The error-model parameters are treated as latent variables and a Maximum Likelihood algorithm that functions by marginalizing the latent variables is obtained. An Expectation-Maximization algorithm that jointly uses the measurements from multiple independent experiments is developed, yielding closed-form expressions for the Gaussian mixture estimators and the noise variance. Numerical simulations demonstrate that our approach yields accurate estimates of both the multivariable nominal system model parameters and the noise variance, even when the error-model non-Gaussian distribution does not correspond to a Gaussian mixture model. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Multivariate Statistics and Data Science, Second Edition)
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22 pages, 1579 KiB  
Article
Spillover Effects of Currency Interactions Across Economic Cycles: A Quantile-VAR Analysis
by Zhuqin Liang and Mohd Tahir Ismail
Symmetry 2025, 17(1), 73; https://doi.org/10.3390/sym17010073 - 4 Jan 2025
Viewed by 905
Abstract
This study employs Markov-Switching Regression (MS-Regression) to model four macroeconomic indicators—US GDP, CPI, interest rate, and unemployment rate—to identify economic crisis cycles, while all indicators provide some level of insight into these cycles, the unemployment rate offers the closest alignment with the actual [...] Read more.
This study employs Markov-Switching Regression (MS-Regression) to model four macroeconomic indicators—US GDP, CPI, interest rate, and unemployment rate—to identify economic crisis cycles, while all indicators provide some level of insight into these cycles, the unemployment rate offers the closest alignment with the actual patterns of economic cycles. Based on the regime identification derived from the unemployment rate, we delineate the time series for expansion and recession periods. Subsequently, we apply the Quantile Vector Autoregression (Quantile-VAR) model to analyze three sets of time series: the entire dataset, the expansion period, and the recession period. Our findings reveal that, under normal conditions, the US dollar exerts the greatest influence on and is most influenced by other currencies, whereas the Australian dollar has the least impact on others. In the extreme lower and upper tails, the mutual influence among the currencies of different countries intensifies, concurrently diminishing the relative influence of the US dollar. Notably, the spillover effects under extreme lower and upper tail conditions are not consistent, as the occurrence of extreme values does not coincide, suggesting an asymmetry in the spillover effects at these quantiles. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Multivariate Statistics and Data Science, Second Edition)
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