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Mathematics
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Advances in Robust and Nonparametric Statistical Techniques for Data Science
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Advances in Robust and Nonparametric Statistical Techniques for Data Science

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

Deadline for manuscript submissions: closed (30 March 2026) | Viewed by 1679

Special Issue Editor

Prof. Dr. Henry Laniado

E-Mail Website
Guest Editor
Department of Mathematics, University of Cauca, Popayan 500001, Colombia
Interests: nonparametric statistics; robust statistics; stochastic orders; survival and reliability

Special Issue Information

Dear Colleagues,

Nonparametric statistical techniques are a set of strategies useful for data analysis in cases where the assumptions necessary to apply parametric methods are not met. These nonparametric methods help to model and analyze practical situations with high-dimensional data in different disciplines with greater versatility while maintaining rigor. Therefore, currently they have become the dominant strategies used in data science.

This Special Issue of Mathematics, ‘Advances in Robust and Nonparametric Statistical Techniques for Data Science’, proposes to collect the recent contributions in theoretical and practical aspects of topics as the following:

  • Goodness-of-fit tests;
  • Nonparametric confidence intervals;
  • Density estimation;
  • Nonparametric regression;
  • Robust statistical methods;
  • Simulation and generation of synthetic data;
  • Statistical methods based on ranks;
  • Supervised and unsupervised classification;
  • Survival and reliability analysis;
  • Robust methods for risk estimation and portfolio selection;
  • Functional data;
  • Identification of outlier data.

Prof. Dr. Henry Laniado
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

  • nonparametric statistics
  • robust statistics
  • data analytics
  • violation of statistical assumptions
  • data science

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Published Papers (2 papers)

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Research

36 pages, 952 KB  
Article
On Minimum Bregman Divergence Inference
by Soumik Purkayastha and Ayanendranath Basu
Mathematics 2026, 14(4), 670; https://doi.org/10.3390/math14040670 - 13 Feb 2026
Viewed by 393
Abstract
The density power divergence (DPD) is a well-studied member of the Bregman divergence family and forms the basis of widely used minimum divergence estimators that balance efficiency and robustness. In this paper, we introduce and study a new sub-class of Bregman divergences, termed [...] Read more.
The density power divergence (DPD) is a well-studied member of the Bregman divergence family and forms the basis of widely used minimum divergence estimators that balance efficiency and robustness. In this paper, we introduce and study a new sub-class of Bregman divergences, termed the exponentially weighted divergence (EWD), designed to generate competitive and practically interpretable inference procedures. The EWD is constructed so that its associated weight function remains bounded within the interval [0, 1], which facilitates a transparent interpretation of robustness through controlled downweighting of low-density observations and avoids excessive influence from high-density points. We develop minimum EWD estimators (MEWDEs) within a general framework accommodating independent but non-homogeneous data, thereby extending classical minimum divergence theory beyond the i.i.d. setting. Under standard regularity conditions, we establish Fisher consistency and asymptotic normality, and we analyze robustness properties through influence function calculations. The EWD framework is further extended to parametric hypothesis testing, for which we derive the asymptotic null distribution of a Bregman divergence-based test statistic. Extensive simulation studies and real-data applications demonstrate that the proposed estimators perform comparably to, and often more robustly than, existing DPD-based procedures, particularly under moderate to heavy contamination, while retaining high efficiency under clean data. Overall, the EWD provides a tractable and interpretable alternative within the Bregman divergence class for robust parametric estimation and testing. Full article
(This article belongs to the Special Issue Advances in Robust and Nonparametric Statistical Techniques for Data Science)
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21 pages, 2131 KB  
Article
Asymptotic Distribution of the Functional Modal Regression Estimator
by Zoulikha Kaid and Mohammed B. Alamari
Mathematics 2025, 13(22), 3637; https://doi.org/10.3390/math13223637 - 13 Nov 2025
Viewed by 645
Abstract
We propose a novel predictor for functional time series (FTS) based on the robust estimation of the modal regression within a functional statistics framework. The robustness of the estimator is incorporated through the L1-estimation of the quantile density. Such consideration improves [...] Read more.
We propose a novel predictor for functional time series (FTS) based on the robust estimation of the modal regression within a functional statistics framework. The robustness of the estimator is incorporated through the L1-estimation of the quantile density. Such consideration improves the precision of conditional mode estimation. A principal theoretical contribution of this work is the establishment of the asymptotic normality of the proposed estimator. This result is of considerable importance, as it provides the foundation for statistical inference, including hypothesis testing and the construction of confidence intervals. Therefore, the obtained asymptotic result enhances the practical usability of the modal regression prediction. On the empirical side, we evaluate the performance of the estimator under various smoothing structures using both simulated and real data. The real data application highlights the ability of the L1-conditional mode predictor to perform robust and reliable short-term forecasts, with very high effectiveness in the analysis of economic data. Full article
(This article belongs to the Special Issue Advances in Robust and Nonparametric Statistical Techniques for Data Science)
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