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Symmetry
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Symmetry/Asymmetry in Goodness-of-Fit Testing and Statistical Inference Using Non-Parametric Approaches
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Symmetry/Asymmetry in Goodness-of-Fit Testing and Statistical Inference Using Non-Parametric Approaches

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 October 2026 | Viewed by 3103

Special Issue Editors

Dr. Chioneso Show Marange

E-Mail Website
Guest Editor
Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein, South Africa
Interests: empirical likelihood method; goodness-of-fit testing; non-parametric statistics; survival analysis
Prof. Dr. Yichuan Zhao

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA
Interests: survival analysis; empirical likelihood method and its application; nonparametric statistics; bioinformatics; ROC curve analysis; Monte Carlo methods; statistical modeling of fuzzy systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Non-parametric methods provide powerful tools for statistical inference, particularly when classical assumptions are violated. Of late, the use of non-parametric techniques such as the empirical likelihood (EL) methodology has led to the development of goodness-of-fit (GoF) tests for various symmetric and asymetric distributions that are superior under several alternatives. Advancing theoretical methodology is therefore crucial for further investigating the strengths and challenges of non-parametric methods in GoF testing. For instance, EL moment-based normality tests may lack power against some symmetric alternatives.

Several parametric estimation methods require data to be consistent with normality, which is symmetric in nature. This assumption is frequently violated in practice, where data may exhibit skewness and kurtosis indicative of underlying asymmetry. Non-parametric methods offer a robust alternative for estimation and inference under these conditions. In biostatistics, issues of symmetry may also arise in the form of censored observations. Specifically, in survival analysis, non-parametric estimators such as the Kaplan–Meier and Turnbull methods address censored data, where the fuzziness in interval-censoring often requires centrality-based imputation methods.

We invite research on how symmetry and asymmetry guide the development of GoF tests, robust estimators, and inference procedures, advancing non-parametric methods in modern statistics. Applications related to biostatistics, epidemiology, and health sciences are encouraged.

In this Special Issue, original research articles and reviews are welcome. Research areas may include (but not limited to) the following:

  • Symmetry and asymmetry in goodness-of-fit testing;
  • Robust and non-parametric methods in statistical inference;
  • Empirical likelihood methods and extensions in goodness-of-fit testing;
  • Non-parametric estimation and survival analysis with censored data;
  • Simulation-based approaches in non-parametric inference;
  • Optimization algorithms for non-parametric inference;
  • Applications of non-parametric methods in biostatistics.

We look forward to receiving your contributions.

Dr. Chioneso Show Marange
Prof. Dr. Yichuan Zhao
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. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • goodness-of-fit testing
  • non-parametric statistics
  • empirical likelihood
  • survival analysis
  • censored data
  • fuzzy
  • test for symmetry
  • optimization algorithms
  • Monte Carlo simulations

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Published Papers (3 papers)

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Research

22 pages, 6300 KB  
Article
The k-Nearest-Neighbor Smoothing Estimator for Functional Least Absolute Relative Error Regression
by Zoulikha Kaid, Fatimah A. Almulhim and Mohammed B. Alamari
Symmetry 2026, 18(5), 790; https://doi.org/10.3390/sym18050790 - 6 May 2026
Viewed by 289
Abstract
In this paper, we propose a new nonparametric method for estimating the regression operator of a scalar response given a functional covariate taking values in a semi-metric space. The estimator is obtained by minimizing the Least Absolute Relative Error (LARE) criterion, which provides [...] Read more.
In this paper, we propose a new nonparametric method for estimating the regression operator of a scalar response given a functional covariate taking values in a semi-metric space. The estimator is obtained by minimizing the Least Absolute Relative Error (LARE) criterion, which provides a scale-invariant and equilibrated measure of prediction accuracy compared with classical regression loss functions. The antisymmetry property of the LARE rule ensures that overestimation and underestimation are penalized in a symmetric relative manner, which improves the robustness when the response variable varies in different scales. Next, the estimator is constructed using k-nearest neighbors (kNN). The combination of the two algorithms allows the procedure to benefit from both the robustness and scale-invariant nature of the LARE criterion and the flexibility and local adaptivity of the kNN smoothing approach, which is particularly suitable for functional or high-dimensional data. As an asymptotic result, we establish the uniform convergence with respect to the number of neighbors (UNN) of the proposed estimator under mild regularity conditions and derive its rate of convergence. We also discuss the selection of the optimal number of neighbors and their impact on performance. The practical effectiveness of the proposed kNN–FLARE regression estimator is illustrated through simulation experiments and an application to near-infrared (NIR) spectrometry data. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Goodness-of-Fit Testing and Statistical Inference Using Non-Parametric Approaches)
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12 pages, 278 KB  
Article
A Transfer Learning Approach to Semiparametric Probit Regression for Interval-Censored Failure Times Data
by Lanxin Cui, Shishun Zhao and Jianhua Cheng
Symmetry 2026, 18(4), 566; https://doi.org/10.3390/sym18040566 - 26 Mar 2026
Viewed by 380
Abstract
Regression analysis of interval-censored failure time data commonly arises in biomedical studies, particularly when the available sample size is limited. Although many methods have been proposed for the semiparametric probit model with interval-censored data, there does not appear to exist an established approach [...] Read more.
Regression analysis of interval-censored failure time data commonly arises in biomedical studies, particularly when the available sample size is limited. Although many methods have been proposed for the semiparametric probit model with interval-censored data, there does not appear to exist an established approach that effectively borrows information from external sources to improve estimation efficiency. Such external information may arise, for example, in clinical trials where an auxiliary dataset from a related population is available but may differ from the target population in certain aspects, leading to heterogeneity between populations. To address this issue, a sieve maximum likelihood estimation procedure is developed for the semiparametric probit model with interval-censored data, and a transfer learning method is proposed to leverage auxiliary information from a source domain to improve estimation efficiency in the target domain while accounting for population heterogeneity. The proposed approach is based on a penalized likelihood formulation and uses monotone splines to approximate the unknown baseline function, providing flexibility in both modeling and computation. Simulation studies show that the proposed estimator substantially improves estimation accuracy compared with methods that rely solely on the target data, particularly when the target sample size is small. An application to an Alzheimer’s disease dataset further illustrates the practical usefulness of the proposed approach in biomedical studies. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Goodness-of-Fit Testing and Statistical Inference Using Non-Parametric Approaches)
63 pages, 1636 KB  
Article
Asymptotic Theory for Multivariate Nonparametric Quantile Regression with Stationary Ergodic Functional Covariates and Missing-at-Random Responses
by Hadjer Belhas, Mustapha Mohammedi and Salim Bouzebda
Symmetry 2026, 18(3), 445; https://doi.org/10.3390/sym18030445 - 4 Mar 2026
Cited by 2 | Viewed by 380
Abstract
Quantiles are among the most fundamental constructs in probability theory and statistics, intrinsically linked to order structures, stochastic dominance, and the principles of robust statistical inference. Although the univariate theory of quantiles is by now classical and well developed, their generalization to multivariate [...] Read more.
Quantiles are among the most fundamental constructs in probability theory and statistics, intrinsically linked to order structures, stochastic dominance, and the principles of robust statistical inference. Although the univariate theory of quantiles is by now classical and well developed, their generalization to multivariate settings remains mathematically subtle and methodologically demanding. In particular, extending the notion of “location within a distribution” beyond one dimension raises delicate questions of geometry, ordering, and equivariance. Within this landscape, the spatial—or geometric—formulation of multivariate quantiles has emerged as a rigorous and conceptually unifying framework capable of reconciling these issues. In this work we advance this paradigm by introducing a kernel-based estimation procedure for nonparametric conditional geometric quantiles of a multivariate response Y∈Rq (q≥2) given a functional covariate X that takes values in an infinite-dimensional space. The data are assumed to form a strictly stationary and ergodic process, while the responses may be subject to a missing-at-random mechanism, a feature of substantial practical relevance. Our analysis establishes strong consistency of the proposed estimator, characterizes its optimal convergence rate, and derives its asymptotic distribution. These limit theorems, in turn, provide the theoretical foundation for constructing asymptotically valid confidence regions and for performing inference in multivariate quantile regression with functional covariates. The theoretical developments rest on natural complexity conditions for the involved functional classes together with mild smoothness and regularity assumptions. This balance between generality and mathematical precision ensures that the resulting methodology is not only robust in a rigorous probabilistic sense but also widely applicable to contemporary problems in high-dimensional and functional data analysis. The proposed methodology is numerically investigated through simulations and is implemented in a real data application. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Goodness-of-Fit Testing and Statistical Inference Using Non-Parametric Approaches)
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