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Mathematics
Special Issues
Statistics: Theories and Applications
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Statistics: Theories and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 10 August 2025 | Viewed by 2971

Special Issue Editors

Prof. Dr. Jiancheng Jiang

E-Mail Website
Guest Editor
Mathematics & Statistics Department, The University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Interests: Bayesian statistics; financial econometrics; interval estimation and hypothesis testing; quality control; quantile regression; statistical learning with big data; survival analysis; regression diagnostics; time series analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Shaoyu Li

E-Mail Website
Guest Editor
Mathematics & Statistics Department, The University of North Carolina at Charlotte, Charlotte, NC 28223, USA
Interests: statistical methods for pairwise distance-based analysis and applications; statistical and computational methods for the analysis of genetics/genomics data, including investigations of gene–gene/gene–environment interactions; genome-wide association studies, systems biology, and epigenome-wide association studies; statistical design for health studies; identification of cell-specific transcriptional variations associated with human diseases
Prof. Dr. Niansheng Tang

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Yunnan University, Kunming 650091, China
Interests: Bayesian statistics; empirical likelihood; nonparametric inference; high-dimensional data analysis; longitudinal data analysis; quantile regression; structural equation models
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are excited to introduce a Special Issue focusing on “Statistics: Theories and Applications.” Today, the field of statistics is experiencing rapid growth fueled by emerging mathematical theories, technological innovations, fresh data streams stemming from contemporary challenges, and numerous connections forged between theory and application. The utilization of statistical theories and applications has become pervasive across various domains including actuarial science, biometrics, biomedical engineering, econometrics, environmental science, and financial markets. This Special Issue aims to highlight the significance and impact of statistics and its application, showcasing the latest advancements in statistical analysis, modeling, learning, and practical implementation. Topics include, but are not limited to, new developments in the following:

  • Bayesian statistics;
  • Model validation;
  • Financial econometrics;
  • Interval estimation and hypothesis testing;
  • Quality control;
  • Quantile regression—univariate and multivariate;
  • Semi- and nonparametric modeling;
  • Statistical learning with big data;
  • Survival analysis;
  • Genetics;
  • Time series analysis—univariate and multivariate;
  • Distributed/parallel computing.

Prof. Dr. Jiancheng Jiang
Dr. Shaoyu Li
Prof. Dr. Niansheng Tang
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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
  • distributed computing
  • variable selection
  • nonparametric smoothing
  • financial time series analysis
  • analysis of genetics data
  • high-dimensional data
  • AI-assisted model validation

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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Research

20 pages, 470 KiB  
Article
A New Class of Probability Distributions via Half-Elliptical Functions
by Lukun Zheng, Ngoc Nguyen and Peyton Erslan
Mathematics 2025, 13(11), 1811; https://doi.org/10.3390/math13111811 - 29 May 2025
Viewed by 264
Abstract
In this paper, we develop a new family of distributions supported on a bounded interval with a probability density function that is constructed from two elliptical arcs. The distribution can take on a variety of shapes and has three basic parameters: minimum, maximum, [...] Read more.
In this paper, we develop a new family of distributions supported on a bounded interval with a probability density function that is constructed from two elliptical arcs. The distribution can take on a variety of shapes and has three basic parameters: minimum, maximum, and mode. Compared to classical bounded distributions such as the beta and triangular distributions, the proposed semi-elliptical family offers greater flexibility in capturing diverse shapes of distributions, in symmetric and asymmetric settings. Its construction from elliptical arcs enables smoother transitions and more natural tail behaviors, making it suitable for applications where classical models may exhibit rigidity or over-simplicity. We give general expression for the density and distribution function of the new distribution. Properties of this distribution are studied and parameter estimation is discussed. Monte Carlo simulation results show the performance of our estimators under many sets of situations. Furthermore, we show the advantages of our distribution over the commonly used triangular distribution in approximating beta distributions. Full article
(This article belongs to the Special Issue Statistics: Theories and Applications)
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15 pages, 602 KiB  
Article
Mixed-Order Fuzzy Time Series Forecast
by Hao Wu, Haiming Long and Jiancheng Jiang
Mathematics 2025, 13(11), 1705; https://doi.org/10.3390/math13111705 - 22 May 2025
Viewed by 365
Abstract
Fuzzy time series forecasting has gained significant attention for its accuracy, robustness, and interpretability, making it widely applicable in practical prediction tasks. In classical fuzzy time series models, the lag order plays a crucial role, with variations in order often leading to markedly [...] Read more.
Fuzzy time series forecasting has gained significant attention for its accuracy, robustness, and interpretability, making it widely applicable in practical prediction tasks. In classical fuzzy time series models, the lag order plays a crucial role, with variations in order often leading to markedly different forecasting results. To obtain the best performance, we propose a mixed-order fuzzy time series model, which incorporates fuzzy logical relationships (FLRs) of different orders into its rule system. This approach mitigates the uncertainty in fuzzy forecasting caused by empty FLRs and FLR groups while fully exploiting the fitting advantages of different-order FLRs. Theoretical analysis is provided to establish the mathematical foundation of the mixed-order model, and its superiority over fixed-order models is demonstrated. Simulation studies reveal that the proposed model outperforms several classical time series models in specific scenarios. Furthermore, applications to real-world datasets, including a COVID-19 case study and a TAIEX financial dataset, validate the effectiveness and applicability of the proposed methodology. Full article
(This article belongs to the Special Issue Statistics: Theories and Applications)
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23 pages, 394 KiB  
Article
Variable Selection for Generalized Single-Index Varying-Coefficient Models with Applications to Synergistic G × E Interactions
by Shunjie Guan, Xu Liu and Yuehua Cui
Mathematics 2025, 13(3), 469; https://doi.org/10.3390/math13030469 - 31 Jan 2025
Viewed by 528
Abstract
Complex diseases such as type 2 diabetes are influenced by both environmental and genetic risk factors, leading to a growing interest in identifying gene–environment (G × E) interactions. A three-step variable selection method for single-index varying-coefficients models was proposed in recent research. This [...] Read more.
Complex diseases such as type 2 diabetes are influenced by both environmental and genetic risk factors, leading to a growing interest in identifying gene–environment (G × E) interactions. A three-step variable selection method for single-index varying-coefficients models was proposed in recent research. This method selects varying and constant-effect genetic predictors, as well as non-zero loading parameters, to identify genetic factors that interact linearly or nonlinearly with a mixture of environmental factors to influence disease risk. In this paper, we extend this approach to a binary response setting given that many complex human diseases are binary traits. We also establish the oracle property for our variable selection method, demonstrating that it performs as well as if the correct sub-model were known in advance. Additionally, we assess the performance of our method through finite-sample simulations with both continuous and discrete gene variables. Finally, we apply our approach to a type 2 diabetes dataset, identifying potential genetic factors that interact with a combination of environmental variables, both linearly and nonlinearly, to influence the risk of developing type 2 diabetes. Full article
(This article belongs to the Special Issue Statistics: Theories and Applications)
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14 pages, 544 KiB  
Article
A Threshold Estimator for Ruin Probability Using the Fourier-Cosine Method in the Wiener–Poisson Risk Model
by Chongkai Xie and Honglong You
Mathematics 2024, 12(18), 2945; https://doi.org/10.3390/math12182945 - 22 Sep 2024
Viewed by 834
Abstract
In this paper, we propose a nonparametric estimator of ruin probability in the Wiener–Poisson risk model based on high-frequency data. The estimator is constructed via the Fourier-cosine method and the threshold technique, and the convergence rate is also studied for a large sample [...] Read more.
In this paper, we propose a nonparametric estimator of ruin probability in the Wiener–Poisson risk model based on high-frequency data. The estimator is constructed via the Fourier-cosine method and the threshold technique, and the convergence rate is also studied for a large sample size. Finally, we verify the effectiveness of our estimator through some simulation studies. Full article
(This article belongs to the Special Issue Statistics: Theories and Applications)
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