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Mathematics
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Mathematical Statistics and Nonparametric Inference
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Mathematical Statistics and Nonparametric Inference

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

Deadline for manuscript submissions: 31 May 2026 | Viewed by 3824

Special Issue Editors

Dr. Hamdy F.F. Mahmoud

E-Mail Website
Guest Editor
Department of Statistics, School of Science, Virginia Tech University, Blacksburg, VA 24061, USA
Interests: semi/nonparametric models; mathematical statistics; change-point(s) detection; spatial and spatial–temporal analysis; functional data analysis
Prof. Dr. Jiancheng Jiang

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, The University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, NC 28223, USA
Interests: Bayesian statistics; financial econometrics; interval estimation and hypothesis testing; nonparametric inference; regularization
Special Issues, Collections and Topics in MDPI journals
Dr. Stefano Bonnini

E-Mail Website
Guest Editor
Department of Economics and Management, University of Ferrara, Via Voltapaletto 11, 44121 Ferrara, Italy
Interests: multivariate analysis; nonparametric statistics; permutation tests; composite indicators
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are excited to invite you to explore and contribute to our Special Issue on Mathematical Statistics and Nonparametric Estimation. This Special Issue is a platform for sharing cutting-edge research and insights on the latest advancements in mathematical statistics and nonparametric techniques and their real-world applications. It focuses on advancements and applications in statistical theory and methodology, emphasizing nonparametric estimation techniques. Nonparametric methods, essential for analyzing data without assuming specific parametric forms, have gained prominence in diverse fields including environmental science, biostatistics, and finance. Contributions will cover both theoretical developments and applied case studies that demonstrate how nonparametric methods offer flexibility and robustness in analyzing complex data structures. Topics of interest include, but are not limited to, innovative estimation techniques, new models for large datasets, change-point detection, and statistical approaches for high-dimensional data. The Special Issue welcomes original research articles, review papers, and methodological contributions that provide new insights or innovative solutions.

Whether you are a researcher, practitioner, or student, we hope this Special Issue will inspire new ideas and foster collaboration within the statistical community. We look forward to your contributions and hope you enjoy the wealth of knowledge presented here.

Warm regards,

Dr. Hamdy F.F. Mahmoud
Prof. Dr. Jiancheng Jiang
Dr. Stefano Bonnini
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 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

  • nonparametric estimation
  • mathematical statistics
  • change-point detection
  • high-dimensional data
  • kernel methods
  • semiparametric models
  • density estimation
  • Bayesian nonparametrics
  • hypothesis testing
  • computational statistics
  • stochastic process
  • Bayesian probability
  • Bernoulli
  • Binomial distribution
  • Central limit
  • Chung–Erdős inequality
  • Circular Law
  • Branching Process
  • Conditional probability
  • convergence for sparse
  • Convergence in probability
  • Convergence of Probability
  • Convergence to the limit
  • Covariance matrix
  • Cumulative distribution function
  • diffusion process
  • uniform distribution
  • Distribution of Sum
  • limit of distribution
  • limit theorem
  • limits of random variables
  • Lindeberg's condition
  • Littlewood's law
  • markov process
  • Markovian process
  • Markov's inequality
  • Maximum likelihood
  • negative binomial distribution
  • nonparametric statistical
  • Pairwise independence
  • Paley–Zygmund inequality
  • Poisson distribution
  • Poisson limit distribution
  • Poisson process
  • Probability axioms
  • probability distribution
  • probability theory
  • Queueing theory
  • random matrices
  • random process
  • random variable
  • random walk

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Published Papers (4 papers)

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Research

16 pages, 327 KB  
Article
Berry–Esseen Bounds of Residual Density Estimators in the First-Order Autoregressive Model with the α-Mixing Errors
by Jiaxin Wang and Tianze Liu
Mathematics 2026, 14(1), 73; https://doi.org/10.3390/math14010073 - 25 Dec 2025
Viewed by 195
Abstract
This study establishes explicit Berry–Esseen bounds for residual kernel density estimators in AR(1) models with α-mixing errors. Since the true innovations are unobservable, we introduce a residual-based estimator f^n(x) and establish its normal approximation under stationarity. By [...] Read more.
This study establishes explicit Berry–Esseen bounds for residual kernel density estimators in AR(1) models with α-mixing errors. Since the true innovations are unobservable, we introduce a residual-based estimator f^n(x) and establish its normal approximation under stationarity. By imposing conditions on the bandwidth, mixing coefficients, and moments, we obtain Kolmogorov distance bounds between the standardized estimator and its Gaussian limit. These bounds explicitly depend on the bandwidth, block parameters, and mixing coefficients. A key corollary quantifies the convergence rate as O(n(2c−2b+a)/4). Our results generalize prior work, advancing theoretical foundations for nonparametric inference in high-dimensional time series. Full article
(This article belongs to the Special Issue Mathematical Statistics and Nonparametric Inference)
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20 pages, 421 KB  
Article
An Inferential Study of Discrete One-Parameter Linear Exponential Distribution Under Randomly Right-Censored Data
by Hanan Baaqeel, Khlood Al-Harbi and Aisha Fayomi
Mathematics 2025, 13(21), 3520; https://doi.org/10.3390/math13213520 - 3 Nov 2025
Viewed by 402
Abstract
Counting data play a critical role in various real-life applications across different scientific fields. This study handles the classical and Bayesian estimation of the one-parameter discrete linear exponential distribution under randomly right-censored data. Maximum likelihood estimators, both point and interval, are derived for [...] Read more.
Counting data play a critical role in various real-life applications across different scientific fields. This study handles the classical and Bayesian estimation of the one-parameter discrete linear exponential distribution under randomly right-censored data. Maximum likelihood estimators, both point and interval, are derived for the unknown parameter. In addition, Bayesian estimators are gained using informative and non-informative priors, assessed under three distinct loss functions: squared error loss, linear exponential loss, and generalized entropy loss. An algorithm for generating randomly right-censored data from the proposed model is also developed. To evaluate the efficiency of the estimators, considerable simulation studies are conducted, revealing that the maximum likelihood and the Bayesian approach under the generalized entropy loss function with a positive weight consistently outperform other methods across all sample sizes, achieving the lowest root mean squared errors. Finally, the discrete linear exponential distribution demonstrates strong applicability in modeling discrete count lifetime data in physical and medical sciences, outperforming related alternative distributions. Full article
(This article belongs to the Special Issue Mathematical Statistics and Nonparametric Inference)
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13 pages, 1545 KB  
Article
Testing the Temperature-Mortality Nonparametric Function Change with an Application to Chicago Mortality
by Hamdy F. F. Mahmoud
Mathematics 2025, 13(15), 2498; https://doi.org/10.3390/math13152498 - 3 Aug 2025
Viewed by 593
Abstract
The relationship between temperature and mortality is well-documented, yet most existing studies assume this relationship remains static over time. This study investigates whether the temperature-mortality association in Chicago from 1987 to 2000 has changed in shape or location of key features, such as [...] Read more.
The relationship between temperature and mortality is well-documented, yet most existing studies assume this relationship remains static over time. This study investigates whether the temperature-mortality association in Chicago from 1987 to 2000 has changed in shape or location of key features, such as change points. We apply nonparametric regression techniques to estimate the temperature-mortality functions for each year using daily mortality and temperature data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) database. A permutation-based test is used to assess whether the shapes of these functions differ across time, while a bootstrap procedure evaluates the consistency of change points. Intensive simulation studies are conducted to evaluate the permutation-based test and bootstrap procedure based on Type I error and power. The proposed tests are compared with F tests in terms of Type I error and power. For the real data set, the analysis finds significant variation in the functional shapes across years, indicating evolving mortality responses to temperature. However, the estimated change points—temperatures associated with peak mortality—remain statistically consistent. These findings suggest that while the population’s overall vulnerability pattern may shift, the temperature threshold linked to maximum mortality has remained stable. This study contributes to understanding the temporal dynamics of climate-sensitive health outcomes and highlights the importance of flexible modeling in public health and climate adaptation planning. Full article
(This article belongs to the Special Issue Mathematical Statistics and Nonparametric Inference)
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36 pages, 442 KB  
Article
Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic Processes
by Sultana Didi and Salim Bouzebda
Mathematics 2025, 13(10), 1587; https://doi.org/10.3390/math13101587 - 12 May 2025
Viewed by 682
Abstract
This study introduces a wavelet-based framework for estimating derivatives of a general regression function within discrete-time, stationary ergodic processes. The analysis focuses on deriving the integrated mean squared error (IMSE) over compact subsets of Rd, while also establishing rates of uniform [...] Read more.
This study introduces a wavelet-based framework for estimating derivatives of a general regression function within discrete-time, stationary ergodic processes. The analysis focuses on deriving the integrated mean squared error (IMSE) over compact subsets of Rd, while also establishing rates of uniform convergence and the asymptotic normality of the proposed estimators. To investigate their asymptotic behavior, we adopt a martingale-based approach specifically adapted to the ergodic nature of the data-generating process. Importantly, the framework imposes no structural assumptions beyond ergodicity, thereby circumventing restrictive dependence conditions. By establishing the limiting behavior of the wavelet estimators under these minimal assumptions, the results extend existing findings for independent data and highlight the flexibility of wavelet methods in more general stochastic settings. Full article
(This article belongs to the Special Issue Mathematical Statistics and Nonparametric Inference)
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