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Stats
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Multivariate Statistics and Applications
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Multivariate Statistics and Applications

A special issue of Stats (ISSN 2571-905X).

Deadline for manuscript submissions: closed (31 October 2022) | Viewed by 18483

Special Issue Editor

Dr. Silvia Romagnoli

E-Mail Website
Guest Editor
Department of statistics, University of Bologna, 40126 Bologna, Italy
Interests: copula methods in finance; stochastic calculus; risk aggregation; multivariate statistics

Special Issue Information

Dear Colleagues,

I am pleased to announce a Special Issue on Multivariate Statistics and Applications. Being that nature is multivariate, it is not surprising that a phenomenon would usually depend on several factors, possibly correlated and whose representation must necessarily involve a useful methodology able to understand and process information in a meaningful fashion. The ambitious aim of this Special Issue is to present a wide range of the newest results on multivariate statistical models, distribution theory, and applications of multivariate statistical methods where applications range from finance and insurance mathematics to medical and industrial statistics and sampling algorithms. Multivariate statistical methods are also essential in communication research and in the developing process of models for online monitoring and control. Copula-based models able to deal with tail dependences of variables are particularly suited to representing special phenomena where natural variables such as wind, air pressure, temperature, and seasonal variations linked to the impact of climate change are involved. Similarly, manuscripts putting forward specific multivariate statistics methodologies which can be useful to practitioners are highly appreciated.

I look forward to receiving your submissions.

Dr. Silvia Romagnoli
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. Stats is an international peer-reviewed open access quarterly 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 1600 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

  • Copula function
  • Principal component analysis
  • Clustering systems
  • Artificial neural network
  • Factor Analysis

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Published Papers (7 papers)

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Research

15 pages, 1094 KiB  
Article
On the Sampling Size for Inverse Sampling
by Daniele Cuntrera, Vincenzo Falco and Ornella Giambalvo
Stats 2022, 5(4), 1130-1144; https://doi.org/10.3390/stats5040067 - 15 Nov 2022
Cited by 1 | Viewed by 2050
Abstract
In the Big Data era, sampling remains a central theme. This paper investigates the characteristics of inverse sampling on two different datasets (real and simulated) to determine when big data become too small for inverse sampling to be used and to examine the [...] Read more.
In the Big Data era, sampling remains a central theme. This paper investigates the characteristics of inverse sampling on two different datasets (real and simulated) to determine when big data become too small for inverse sampling to be used and to examine the impact of the sampling rate of the subsamples. We find that the method, using the appropriate subsample size for both the mean and proportion parameters, performs well with a smaller dataset than big data through the simulation study and real-data application. Different settings related to the selection bias severity are considered during the simulation study and real application. Full article
(This article belongs to the Special Issue Multivariate Statistics and Applications)
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11 pages, 288 KiB  
Article
A Log-Det Heuristics for Covariance Matrix Estimation: The Analytic Setup
by Enrico Bernardi and Matteo Farnè
Stats 2022, 5(3), 606-616; https://doi.org/10.3390/stats5030037 - 5 Jul 2022
Viewed by 2079
Abstract
This paper studies a new nonconvex optimization problem aimed at recovering high-dimensional covariance matrices with a low rank plus sparse structure. The objective is composed of a smooth nonconvex loss and a nonsmooth composite penalty. A number of structural analytic properties of the [...] Read more.
This paper studies a new nonconvex optimization problem aimed at recovering high-dimensional covariance matrices with a low rank plus sparse structure. The objective is composed of a smooth nonconvex loss and a nonsmooth composite penalty. A number of structural analytic properties of the new heuristics are presented and proven, thus providing the necessary framework for further investigating the statistical applications. In particular, the first and the second derivative of the smooth loss are obtained, its local convexity range is derived, and the Lipschitzianity of its gradient is shown. This opens the path to solve the described problem via a proximal gradient algorithm. Full article
(This article belongs to the Special Issue Multivariate Statistics and Applications)
14 pages, 1158 KiB  
Article
Omnibus Tests for Multiple Binomial Proportions via Doubly Sampled Framework with Under-Reported Data
by Dewi Rahardja
Stats 2022, 5(2), 408-421; https://doi.org/10.3390/stats5020024 - 23 Apr 2022
Viewed by 2622
Abstract
Previously, Rahardja (2020) paper (in the first reference list) developed a (pairwise) multiple comparison procedure (MCP) to determine which (proportions) pairs of Multiple Binomial Proportions (with under-reported data), the significant differences came from. Generally, such an MCP test (developed by Rahardja, 2020) is [...] Read more.
Previously, Rahardja (2020) paper (in the first reference list) developed a (pairwise) multiple comparison procedure (MCP) to determine which (proportions) pairs of Multiple Binomial Proportions (with under-reported data), the significant differences came from. Generally, such an MCP test (developed by Rahardja, 2020) is the second part of a two-stage sequential test. In this paper, we derived two omnibus tests (i.e., the overall equality of multiple proportions test) as the first part of the above two-stage sequential test (with under-reported data), in general. Using two likelihood-based approaches, we acquire two Wald-type (Omnibus) tests to compare Multiple Binomial Proportions (in the presence of under-reported data). Our closed-form algorithm is easy to implement and not computationally burdensome. We applied our algorithm to a vehicle-accident data example. Full article
(This article belongs to the Special Issue Multivariate Statistics and Applications)
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42 pages, 6219 KiB  
Article
Properties and Limiting Forms of the Multivariate Extended Skew-Normal and Skew-Student Distributions
by Christopher J. Adcock
Stats 2022, 5(1), 270-311; https://doi.org/10.3390/stats5010017 - 9 Mar 2022
Cited by 2 | Viewed by 2480
Abstract
This paper is concerned with the multivariate extended skew-normal [MESN] and multivariate extended skew-Student [MEST] distributions, that is, distributions in which the location parameters of the underlying truncated distributions are not zero. The extra parameter leads to greater variability in the moments and [...] Read more.
This paper is concerned with the multivariate extended skew-normal [MESN] and multivariate extended skew-Student [MEST] distributions, that is, distributions in which the location parameters of the underlying truncated distributions are not zero. The extra parameter leads to greater variability in the moments and critical values, thus providing greater flexibility for empirical work. It is reported in this paper that various theoretical properties of the extended distributions, notably the limiting forms as the magnitude of the extension parameter, denoted τ in this paper, increases without limit. In particular, it is shown that as τ→−∞, the limiting forms of the MESN and MEST distributions are different. The effect of the difference is exemplified by a study of stockmarket crashes. A second example is a short study of the extent to which the extended skew-normal distribution can be approximated by the skew-Student. Full article
(This article belongs to the Special Issue Multivariate Statistics and Applications)
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18 pages, 352 KiB  
Article
Multivariate Threshold Regression Models with Cure Rates: Identification and Estimation in the Presence of the Esscher Property
by Mei-Ling Ting Lee and George A. Whitmore
Stats 2022, 5(1), 172-189; https://doi.org/10.3390/stats5010012 - 11 Feb 2022
Cited by 3 | Viewed by 2464
Abstract
The first hitting time of a boundary or threshold by the sample path of a stochastic process is the central concept of threshold regression models for survival data analysis. Regression functions for the process and threshold parameters in these models are multivariate combinations [...] Read more.
The first hitting time of a boundary or threshold by the sample path of a stochastic process is the central concept of threshold regression models for survival data analysis. Regression functions for the process and threshold parameters in these models are multivariate combinations of explanatory variates. The stochastic process under investigation may be a univariate stochastic process or a multivariate stochastic process. The stochastic processes of interest to us in this report are those that possess stationary independent increments (i.e., Lévy processes) as well as the Esscher property. The Esscher transform is a transformation of probability density functions that has applications in actuarial science, financial engineering, and other fields. Lévy processes with this property are often encountered in practical applications. Frequently, these applications also involve a ‘cure rate’ fraction because some individuals are susceptible to failure and others not. Cure rates may arise endogenously from the model alone or exogenously from mixing of distinct statistical populations in the data set. We show, using both theoretical analysis and case demonstrations, that model estimates derived from typical survival data may not be able to distinguish between individuals in the cure rate fraction who are not susceptible to failure and those who may be susceptible to failure but escape the fate by chance. The ambiguity is aggravated by right censoring of survival times and by minor misspecifications of the model. Slightly incorrect specifications for regression functions or for the stochastic process can lead to problems with model identification and estimation. In this situation, additional guidance for estimating the fraction of non-susceptibles must come from subject matter expertise or from data types other than survival times, censored or otherwise. The identifiability issue is confronted directly in threshold regression but is also present when applying other kinds of models commonly used for survival data analysis. Other methods, however, usually do not provide a framework for recognizing or dealing with the issue and so the issue is often unintentionally ignored. The theoretical foundations of this work are set out, which presents new and somewhat surprising results for the first hitting time distributions of Lévy processes that have the Esscher property. Full article
(This article belongs to the Special Issue Multivariate Statistics and Applications)
18 pages, 3669 KiB  
Article
All-NBA Teams’ Selection Based on Unsupervised Learning
by João Vítor Rocha da Silva and Paulo Canas Rodrigues
Stats 2022, 5(1), 154-171; https://doi.org/10.3390/stats5010011 - 9 Feb 2022
Cited by 3 | Viewed by 3682
Abstract
All-NBA Teams’ selections have great implications for the players’ and teams’ futures. Since contract extensions are highly related to awards, which can be seen as indexes that measure a players’ production in a year, team selection is of mutual interest for athletes and [...] Read more.
All-NBA Teams’ selections have great implications for the players’ and teams’ futures. Since contract extensions are highly related to awards, which can be seen as indexes that measure a players’ production in a year, team selection is of mutual interest for athletes and franchises. In this paper, we are interested in studying the current selection format. In particular, this study aims to: (i) identify the factors that are taken into consideration by voters when choosing the three All-NBA Teams; and (ii) suggest a new selection format to evaluate players’ performances. Average game-related statistics of all active NBA players in regular seasons from 2013-14 to 2018-19, were analyzed using LASSO (Logistic) Regression and Principal Component Analysis (PCA). It was possible: (i) to determine an All-NBA player profile; (ii) to determine that this profile can cause a misrepresentation of players’ modern and versatile gameplay styles; and (iii) to suggest a new way to evaluate and select players, through PCA. As the results of this paper a model is presented that may help not only the NBA to better evaluate players, but any basketball league; it also may be a source to researchers that aim to investigate player performance, development, and their impact over many seasons. Full article
(This article belongs to the Special Issue Multivariate Statistics and Applications)
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16 pages, 512 KiB  
Article
Assessment of Climate Change in Italy by Variants of Ordered Correspondence Analysis
by Assuntina Cembalo, Rosaria Lombardo, Eric J. Beh, Gianpaolo Romano, Michele Ferrucci and Francesca M. Pisano
Stats 2021, 4(1), 146-161; https://doi.org/10.3390/stats4010012 - 1 Mar 2021
Viewed by 2375
Abstract
This paper explores climate changes in Italy over the last 30 years. The data come from the European observation gridded dataset and are concerned with the temperature throughout the country. We focus our attention on two Italian regions (Lombardy in northern Italy and [...] Read more.
This paper explores climate changes in Italy over the last 30 years. The data come from the European observation gridded dataset and are concerned with the temperature throughout the country. We focus our attention on two Italian regions (Lombardy in northern Italy and Campania in southern Italy) and on two particular years roughly thirty years apart (1986 and 2015). Our primary aim is to assess the most important changes in temperature in Italy using some variants of correspondence analysis for ordered categorical variables. Such variants are based on a decomposition method using orthogonal polynomials instead of singular vectors and allow one to easily classify the meteorological station observations. A simulation study, based on bootstrap sampling, is undertaken to demonstrate the reliability of the results. Full article
(This article belongs to the Special Issue Multivariate Statistics and Applications)
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