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Mathematics
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Computational Statistics and Data Analysis, 3rd Edition
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Computational Statistics and Data Analysis, 3rd Edition

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

Deadline for manuscript submissions: 31 January 2027 | Viewed by 3245

Special Issue Editor

Prof. Dr. Gaorong Li

E-Mail Website
Guest Editor
School of Statistics, Beijing Normal University, Beijing 100875, China
Interests: high-dimensional statistics; nonparametric statistics and complex data analysis; model/variable selection; statistical learning; causal inference; longitudinal/panel data analysis; measurement error model; empirical likelihood
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

With the development of scientific techniques, computational statistics and data analysis have become more and more important in diverse areas of science, engineering, and humanities, ranging from genomics and health sciences to economics, finance, and machine learning. To analyze the real data in these fields, statistical methodologies and computing for data analysis are fundamental to statistical modeling and data analysis. In this Special Issue, we are looking for high-quality research papers in computational statistics and data analysis. We invite investigators to contribute original research articles as well as review articles that will stimulate the development of statistical methodology and applications concerning the data analysis.

Prof. Dr. Gaorong Li
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 250 words) can be sent to the Editorial Office for assessment.

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

  • bootstrapping
  • classification
  • data analytical strategies and methodologies applied in biostatistics
  • dimension reduction of high-dimensional data analysis
  • large-scale inference for Gaussian graphical models and covariance estimation
  • longitudinal/panel data analysis
  • massive networks
  • medical statistics
  • nonparametric and semiparametric models
  • optimal portfolio
  • robust statistics
  • statistical methodology and computing for data analysis
  • statistical methodology and computing for noise data, such as measurement error data, missing data etc.
  • sufficient dimension reduction methods in regression analysis variable/model selection for high-dimensional data

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Related Special Issues

Published Papers (5 papers)

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Research

18 pages, 464 KB  
Article
Lower Bounds for the Asymptotic Relative Efficiency of Huber Regression
by Xiaoyi Wang and Le Zhou
Mathematics 2026, 14(7), 1138; https://doi.org/10.3390/math14071138 - 28 Mar 2026
Viewed by 391
Abstract
Huber regression serves as a prominent robust alternative to ordinary least squares (OLS), particularly in the presence of heavy-tailed error distributions. While the asymptotic relative efficiency (ARE) of Huber regression is well documented for the standard normal distribution, its worst-case efficiency across the [...] Read more.
Huber regression serves as a prominent robust alternative to ordinary least squares (OLS), particularly in the presence of heavy-tailed error distributions. While the asymptotic relative efficiency (ARE) of Huber regression is well documented for the standard normal distribution, its worst-case efficiency across the class of all continuous and symmetric error distributions remains an important theoretical question. In this paper, we establish positive lower bounds for the ARE of Huber regression relative to OLS. By strategically selecting the robustification parameter based on the moments or quantiles of the error distribution, we first prove that the ARE is uniformly bounded away from zero across all continuous and symmetric error distributions. This result guarantees a baseline level of efficiency for Huber regression, sharing a similar theoretical spirit with the celebrated lower bound of the Wilcoxon rank estimator. Utilizing the empirical process theory, we further establish that the relative efficiency of Huber regression remains unchanged if the theoretical tuning parameter is replaced by an estimator with a suitable convergence rate. Simulation studies are conducted to examine the performance of Huber regression under the proposed tuning strategies. Full article
(This article belongs to the Special Issue Computational Statistics and Data Analysis, 3rd Edition)
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33 pages, 662 KB  
Article
The Asymmetric Bimodal Normal Distribution: A Tractable Mixture Model for Skewed and Bimodal Data
by Hassan S. Bakouch, Hugo S. Salinas, Çağatay Çetinkaya, Shaykhah Aldossari, Amira F. Daghestani and John L. Santibáñez
Mathematics 2026, 14(5), 901; https://doi.org/10.3390/math14050901 - 6 Mar 2026
Viewed by 585
Abstract
We study a parsimonious constrained two-component Gaussian mixture with symmetric locations ±λ and unequal weights controlled by α∈[−1,1]; we refer to this family as the asymmetric bimodal normal. The constraint eliminates label switching and [...] Read more.
We study a parsimonious constrained two-component Gaussian mixture with symmetric locations ±λ and unequal weights controlled by α∈[−1,1]; we refer to this family as the asymmetric bimodal normal. The constraint eliminates label switching and yields an identifiable parametrization for λ>0, while noting the boundary degeneracy at λ=0 where α is not identifiable. We derive closed-form analytical expressions for the density and distribution functions, an equivalent constructive representation (useful for simulation and interpretation), explicit moment formulas, and conditions distinguishing unimodality from bimodality. For inference, we develop maximum likelihood estimation with observed information standard errors and provide numerically stable fits via a block-coordinate quasi-Newton routine using method of moments initial values. A Monte Carlo simulation study across representative parameter settings evaluates bias and root mean squared error, and examines the behavior of Hessian-based standard error estimates, highlighting regimes where the observed information becomes ill-conditioned under weak separation. Empirical analyses, chemical calibration deviations from the National Institute of Standards and Technology and a regression example with asymmetric errors, show competitive or superior fit and interpretability relative to skewed normal alternatives, asymmetric Laplace models, and unconstrained Gaussian mixtures, with consistent advantages under model comparison using the Akaike information criterion and the Bayesian information criterion. Full article
(This article belongs to the Special Issue Computational Statistics and Data Analysis, 3rd Edition)
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21 pages, 2096 KB  
Article
Computation of Population Variance Estimation in Simple Random Sampling Structures by Developing Generalized Estimator
by Ahlem Djebar, Abdulaziz S. Alghamdi, Manahil SidAhmed Mustafa and Sohaib Ahmad
Mathematics 2026, 14(2), 375; https://doi.org/10.3390/math14020375 - 22 Jan 2026
Cited by 1 | Viewed by 463
Abstract
The correct estimation of the population variance plays a vital role in the sampling procedure in surveys, especially when simple random sampling techniques are used. In this work, we propose a new generalized statistical inference in order to estimate the population variance using [...] Read more.
The correct estimation of the population variance plays a vital role in the sampling procedure in surveys, especially when simple random sampling techniques are used. In this work, we propose a new generalized statistical inference in order to estimate the population variance using auxiliary information. We can use the relationship between the study variable and the auxiliary variable to construct a novel generalized class of estimators that is better performing in terms of minimum mean squared error (MSE) and has a higher percentage of relative efficiency than the traditional estimators. The proposed methodology is based on the existing methods of inference with the introduction of modifications to cover the known population parameters of additional auxiliary variables, like the mean, the coefficient of variation, skewness, or kurtosis. Theoretical properties such as bias and mean squared error are obtained with regard to the first-order approximation. The performance of the proposed class of estimators is checked by comparing with that of the classical variance estimators in different population conditions based on real-life data sets and a simulation study. The numerical findings have indicated that the suggested class of estimators is more effective compared to classical methods, especially in cases where there is a very high linear correlation between the auxiliary and the study variables. Also, the estimators are robust, as confirmed using various sample sizes and population structures. The research has made a significant contribution to the development of statistical procedures in survey sampling because the practical and efficient tools provided in the study were useful in estimating the variance. The results have been of great importance when applied by researchers and practitioners active in large-scale surveys. Subsequently, in the case of efficient utilization of auxiliary information, it is feasible to have more accurate and cost-effective statistical inference. Full article
(This article belongs to the Special Issue Computational Statistics and Data Analysis, 3rd Edition)
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20 pages, 5378 KB  
Article
Data-Dependent Weighted E-Value Aggregation for Fusion Learning
by Jiahang Gao, Hongyu Chen and Guanxun Li
Mathematics 2026, 14(1), 88; https://doi.org/10.3390/math14010088 - 26 Dec 2025
Viewed by 540
Abstract
We propose a data-dependent weighted e-value aggregation framework for synthesizing discoveries across partially overlapping studies. The key idea is to convert within study p-value-based multiple testing results into e-values and aggregate them using data-dependent leave-one-out weights, thereby mitigating the power loss associated [...] Read more.
We propose a data-dependent weighted e-value aggregation framework for synthesizing discoveries across partially overlapping studies. The key idea is to convert within study p-value-based multiple testing results into e-values and aggregate them using data-dependent leave-one-out weights, thereby mitigating the power loss associated with naive averaging. We show that applying the e-Benjamini–Hochberg procedure to the aggregated e-values yields finite-sample control of the global false discovery rate under standard conditions. Simulation studies and real-data analyses demonstrate the effectiveness and practical advantages of the proposed methods. Full article
(This article belongs to the Special Issue Computational Statistics and Data Analysis, 3rd Edition)
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12 pages, 657 KB  
Article
Distribution of Distances Between Random Vectors and Two Fixed Points
by John Lawrence
Mathematics 2026, 14(1), 11; https://doi.org/10.3390/math14010011 - 20 Dec 2025
Viewed by 608
Abstract
Suppose x→ and y→ are two arbitrary fixed points in d-dimensional space and Z→ is a random vector with a known probability density. It is desired in some applications to find the joint probability distribution function for the distance [...] Read more.
Suppose x→ and y→ are two arbitrary fixed points in d-dimensional space and Z→ is a random vector with a known probability density. It is desired in some applications to find the joint probability distribution function for the distance between x→ and Z→ and the distance between y→ and Z→. This calculation has applications in signal processing, goodness-of-fit testing and two-sample testing. In this article, the efficient numerical calculation of the probability distribution is illustrated. The calculation reduces to the sum of two separate integrals where each integral is over a spherical cap. This is achieved by a transformation of the complex spherical intersection region into a sum of integrals over hypercubes via a carefully constructed variable change. The general approach applies to any application where integrals over a region defined by a spherical cap need to be evaluated. Full article
(This article belongs to the Special Issue Computational Statistics and Data Analysis, 3rd Edition)
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