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Axioms
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New Perspectives in Mathematical Statistics
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New Perspectives in Mathematical Statistics

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 1 November 2024 | Viewed by 4629

Special Issue Editors

Dr. Xiaonan Zhu

E-Mail Website
Guest Editor
Department of Mathematics, University of North Alabama, Florence, AL, USA
Interests: multivariate statistical analysis; (closed) skew normal distribution; stochastic frontier models under skew normal settings; machine learning and deep learning integration in statistics; copulas theory
Prof. Dr. Jong-Min Kim

E-Mail Website
Guest Editor
Statistics Discipline, Division of Science and Mathematics, University of Minnesota at Morris, Morris, MN 56267, USA
Interests: probability and stochastic processes; Functional Data Analysis; financial time series
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to showcase cutting-edge developments and innovative approaches that push the boundaries of traditional methodologies in mathematical statistics. In an era characterized by rapidly advancing technology, increased data complexity, and interdisciplinary collaborations, this Special Issue seeks to highlight the new perspectives of mathematical statistics and its role in addressing contemporary challenges. Contributions to this Special Issue will present novel methods, theoretical advancements, and practical applications aimed at advancing the field of mathematical statistics. By emphasizing new perspectives in mathematical statistics, our objective is to inspire researchers to explore unconventional avenues and foster a deeper understanding of statistics and their relevance to modern challenges across various disciplines.

This Special Issue will address a diverse range of topics, including but not limited to Bayesian statistics, statistical analysis for high-dimensional data, nonparametric statistics and distribution-free methods, machine learning integration in statistics, robust statistical inference, spatial statistics, time series analysis, statistical inference, and computational statistics.

We hope that this initiative will be attractive to researchers in the above areas. Researchers are invited to share their insights, methods, and findings, providing an overview of the latest trends and emerging perspectives in mathematical statistics, and we encourage you to submit your current results to be included in the Special Issue.

Dr. Xiaonan Zhu
Prof. Dr. Jong-Min Kim
Guest Editors

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

  • Bayesian statistics
  • statistical analysis for high-dimensional data
  • nonparametric statistics
  • distribution-free methods
  • machine learning
  • robust statistics
  • spatial statistics
  • time series analysis
  • statistical inference
  • computational statistics

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Published Papers (5 papers)

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Research

13 pages, 2478 KiB  
Article
The Geometry of Dynamic Time-Dependent Best–Worst Choice Pairs
by Sasanka Adikari, Norou Diawara and Haim Bar
Axioms 2024, 13(9), 641; https://doi.org/10.3390/axioms13090641 - 19 Sep 2024
Viewed by 203
Abstract
There has been increasing interest in best–worst discrete choice experiments (BWDCEs) in health economics, transportation research, and other fields over the last few years. BWDCEs have distinct advantages compared to other measurement approaches in discrete choice experiments (DCEs). A systematic study of best–worst [...] Read more.
There has been increasing interest in best–worst discrete choice experiments (BWDCEs) in health economics, transportation research, and other fields over the last few years. BWDCEs have distinct advantages compared to other measurement approaches in discrete choice experiments (DCEs). A systematic study of best–worst (BW) choice pairs can be traced back to the 1990s. Recently, new ideas have been introduced to the subject. Calculating utility helps measure the attractiveness of BW choices. The goal of this paper is twofold. First, we extend the idea of the BW choice pair to include dynamic, time-dependent transition probability and capture utility at each time and for each choice pair. Second, we used the geometry of BW choice pairs to capture the correlations among them and to characterize and clarify the BW choice pairs in the network, where properties can be derived within each class. This paper discusses BWDCEs, the probability transition matrix of choices over time, and the utility function. The proposed network classification for BW choice pairs is laid out. A detailed simulated example is presented, and the results are compared with the classical K-means classification. Full article
(This article belongs to the Special Issue New Perspectives in Mathematical Statistics)
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25 pages, 899 KiB  
Article
Comparative Analysis of Exact Methods for Testing Equivalence of Prevalences in Bilateral and Unilateral Combined Data with and without Assumptions of Correlation
by Shuyi Liang and Changxing Ma
Axioms 2024, 13(7), 430; https://doi.org/10.3390/axioms13070430 - 26 Jun 2024
Viewed by 903
Abstract
In clinical studies focusing on paired body parts, diseases can manifest on either both sides (bilateral) or just one side (unilateral) of the organs. Consequently, the data in these studies may consist of records from both bilateral and unilateral cases. There are two [...] Read more.
In clinical studies focusing on paired body parts, diseases can manifest on either both sides (bilateral) or just one side (unilateral) of the organs. Consequently, the data in these studies may consist of records from both bilateral and unilateral cases. There are two different methods of analyzing the data. One of the methods is assuming that the pair of measurements from the same subject are independent, while the other considers the correlation between paired organs. In terms of the homogeneity test of proportions, asymptotic methods have been proposed given the moderate size of data. This article extends the existing work by proposing exact methods to deal with the scenarios when the sample size is small and asymptotic methods perform poorly. The impact of the correlation assumption is also explored. Among the proposed methods, calculating p-values by replacing unknown parameters with estimated values while accounting for the correlation is recommended based on its satisfactory type I error controls and statistical powers. The proposed methods are applied to three real examples for illustration. Full article
(This article belongs to the Special Issue New Perspectives in Mathematical Statistics)
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19 pages, 293 KiB  
Article
Extensions of Some Statistical Concepts to the Complex Domain
by Arak M. Mathai
Axioms 2024, 13(7), 422; https://doi.org/10.3390/axioms13070422 - 22 Jun 2024
Viewed by 388
Abstract
This paper deals with the extension of principal component analysis, canonical correlation analysis, the Cramer–Rao inequality, and a few other statistical concepts in the real domain to the corresponding complex domain. Optimizations of Hermitian forms under a linear constraint, a bilinear form under [...] Read more.
This paper deals with the extension of principal component analysis, canonical correlation analysis, the Cramer–Rao inequality, and a few other statistical concepts in the real domain to the corresponding complex domain. Optimizations of Hermitian forms under a linear constraint, a bilinear form under Hermitian-form constraints, and similar maxima/minima problems in the complex domain are discussed. Some vector/matrix differential operators are developed to handle the above types of problems. These operators in the complex domain and the optimization problems in the complex domain are believed to be new and novel. These operators will also be useful in maximum likelihood estimation problems, which will be illustrated in the concluding remarks. Detailed steps are given in the derivations so that the methods are easily accessible to everyone. Full article
(This article belongs to the Special Issue New Perspectives in Mathematical Statistics)
19 pages, 653 KiB  
Article
Weighted Least Squares Regression with the Best Robustness and High Computability
by Yijun Zuo and Hanwen Zuo
Axioms 2024, 13(5), 295; https://doi.org/10.3390/axioms13050295 - 27 Apr 2024
Viewed by 1172
Abstract
A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual as equally important, the new procedure exponentially down-weights squared residuals that lie far away from the [...] Read more.
A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual as equally important, the new procedure exponentially down-weights squared residuals that lie far away from the cloud of all residuals and assigns a constant weight (one) to squared residuals that lie close to the center of the squared-residual cloud. The new procedure can keep a good balance between robustness and efficiency; it possesses the highest breakdown point robustness for any regression equivariant procedure, being much more robust than the classic least squares, yet much more efficient than the benchmark robust method, the least trimmed squares (LTS) of Rousseeuw. With a smooth weight function, the new procedure could be computed very fast by the first-order (first-derivative) method and the second-order (second-derivative) method. Assertions and other theoretical findings are verified in simulated and real data examples. Full article
(This article belongs to the Special Issue New Perspectives in Mathematical Statistics)
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12 pages, 310 KiB  
Article
Personalized Treatment Policies with the Novel Buckley-James Q-Learning Algorithm
by Jeongjin Lee and Jong-Min Kim
Axioms 2024, 13(4), 212; https://doi.org/10.3390/axioms13040212 - 25 Mar 2024
Cited by 1 | Viewed by 1164
Abstract
This research paper presents the Buckley-James Q-learning (BJ-Q) algorithm, a cutting-edge method designed to optimize personalized treatment strategies, especially in the presence of right censoring. We critically assess the algorithm’s effectiveness in improving patient outcomes and its resilience across various scenarios. Central to [...] Read more.
This research paper presents the Buckley-James Q-learning (BJ-Q) algorithm, a cutting-edge method designed to optimize personalized treatment strategies, especially in the presence of right censoring. We critically assess the algorithm’s effectiveness in improving patient outcomes and its resilience across various scenarios. Central to our approach is the innovative use of the survival time to impute the reward in Q-learning, employing the Buckley-James method for enhanced accuracy and reliability. Our findings highlight the significant potential of personalized treatment regimens and introduce the BJ-Q learning algorithm as a viable and promising approach. This work marks a substantial advancement in our comprehension of treatment dynamics and offers valuable insights for augmenting patient care in the ever-evolving clinical landscape. Full article
(This article belongs to the Special Issue New Perspectives in Mathematical Statistics)
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