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Dear Colleagues,

The Special Issue is dedicated to exploring the latest advances in the Statistics area of Mathematics that are innovative in either their theoretical, methodological, or applicability approach. The potential topics of this Special Issue incorporate but are not limited to, non-parametric statistics; functional data analysis; fuzzy and random sets; multivariate statistics; classification: supervised and clustering, including machine learning techniques, robust statistics, hypothesis testing, and time series analysis.

Prof. Dr. Alicia Nieto-Reyes
Guest Editor

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Keywords

non-parametric statistics
functional data analysis
fuzzy and random sets
multivariate statistics
classification

Published Papers (2 papers)

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Research

7 pages, 246 KiB

Open AccessCommunication

(Re-)Reading Sklar (1959)—A Personal View on Sklar’s Theorem

by Gery Geenens

Mathematics 2024, 12(3), 380; https://doi.org/10.3390/math12030380 - 24 Jan 2024

Cited by 1 | Viewed by 653

Abstract

In this short communication, I share some personal thoughts on Sklar’s theorem and copulas after reading the original paper (Sklar, 1959) in French. After providing a literal translation of Sklar’s original statements, I argue that the modern version of ‘Sklar’s theorem’ given in most references has a slightly different emphasis, which may lead to subtly different interpretations. In particular, with no reference to the subcopula, modern ‘Sklar’s theorem’ does not provide the clues to fully appreciate when the copula representation of a distribution may form a valid basis for dependence modelling and when it may not. Full article

(This article belongs to the Special Issue Advances in Statistics: Theory, Methodology, Applications and Data Analysis, 2nd Edition)

25 pages, 400 KiB

Open AccessArticle

A Posterior p-Value for Homogeneity Testing of the Three-Sample Problem

by Yufan Wang and Xingzhong Xu

Mathematics 2023, 11(18), 3849; https://doi.org/10.3390/math11183849 - 8 Sep 2023

Viewed by 636

Abstract

In this paper, we study a special kind of finite mixture model. The sample drawn from the model consists of three parts. The first two parts are drawn from specified density functions,

f_{1}

and

f_{2}

, while the third one is [...] Read more.

In this paper, we study a special kind of finite mixture model. The sample drawn from the model consists of three parts. The first two parts are drawn from specified density functions,

f_{1}

and

f_{2}

, while the third one is drawn from the mixture. A problem of interest is whether the two functions,

f_{1}

and

f_{2}

, are the same. To test this hypothesis, we first define the regular location and scale family of distributions and assume that

f_{1}

and

f_{2}

are regular density functions. Then the hypothesis transforms to the equalities of the location and scale parameters, respectively. To utilize the information in the sample, we use Bayes’ theorem to obtain the posterior distribution and give the sampling method. We then propose the posterior p-value to test the hypothesis. The simulation studies show that our posterior p-value largely improves the power in both normal and logistic cases and nicely controls the Type-I error. A real halibut dataset is used to illustrate the validity of our method. Full article

(This article belongs to the Special Issue Advances in Statistics: Theory, Methodology, Applications and Data Analysis, 2nd Edition)

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