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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 1777

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

Published Papers (2 papers)

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Research

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 565
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
Viewed by 843
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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