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: 20 July 2025 | Viewed by 1162

Special Issue Editors


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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

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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
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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

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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 (1 paper)

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Research

36 pages, 442 KiB  
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 140
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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