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Mathematics
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Parametric and Nonparametric Statistics: From Theory to Applications
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Parametric and Nonparametric Statistics: From Theory to Applications

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

Deadline for manuscript submissions: 31 March 2025 | Viewed by 6477

Special Issue Editor

Prof. Dr. Joseph Ngatchou-Wandji

E-Mail Website
Guest Editor
1. EHESP French School of Public Health, 35043 Rennes, France
2. Institut Élie Cartan de Lorraine, University of Lorraine, 54052 Vandoeuvre-Lès-Nancy, France
Interests: parametric and non-parametric estimation and testing in time series; study of trend tests in health data; survival estimate; classification

Special Issue Information

Dear Colleagues,

Parametric methods in statistics are based on hypothetical parametric models of the data under study. This requires that the assumptions made about these models be verified for the reliability of the results obtained with these methods to be confirmed. In contrast, nonparametric methods in statistics are not based on hypothetical models. They can be used even if the assumptions required for the parametric methods are not met. For choosing between parametric or nonparametric methods one should consider several criteria about the data and the assumptions, and ensure to check the validity of these assumptions. Semiparametric methods can be seen as those combining parametric and nonparametric principles and techniques.

Parametric and nonparametric methods in statistics are widely studied in literature. Their theoretical developments and practical applications are growing steadily. This Special Issue, entitled “Parametric and Nonparametric Statistics: From Theory to Applications”, is dedicated to topics involving recent developments in parametric, semiparametric and nonparametric statistics, and their application to various scientific domains such as time series, regression, empirical processes, high-dimensional data, data mining., econometrics, finance, biology, signal, image processing, etc. Thus, this Special Issue is a platform for researchers and readers interested to these topics.

We invite papers on parametric or nonparametric estimation, on parametric or nonparametric tests, as well as those on semiparametric methods. This includes review papers, theoretical and methodological papers, and also numerical papers treating simulated and/or real data with parametric, nonparametric or semiparametric statistical methods.

Prof. Dr. Joseph Ngatchou-Wandji
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 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • empirical processes, high-dimensional data, data mining
  • extremes
  • records
  • time series
  • regression
  • econometrics
  • signal processing
  • parametric methods
  • nonparametric methods
  • semiparametric methods
  • rank statistics
  • order statistics
  • robustness
  • renewal processes
  • functional estimation

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Published Papers (6 papers)

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Research

14 pages, 886 KiB  
Article
Applying the Laplace Transform Procedure, Testing Exponentiality against the NBRUmgf Class
by Naglaa A. Hassan, Mayar M. Said, Rasha Abd El-Wahab Attwa and Taha Radwan
Mathematics 2024, 12(13), 2045; https://doi.org/10.3390/math12132045 - 30 Jun 2024
Viewed by 569
Abstract
This paper addresses a hypothesis testing problem for comparing exponentially distributed data against a new class termed “New Better than Renewal Used in Moment Generating Function” (NBRUmgf). A measure of departure from exponentiality is constructed [...] Read more.
This paper addresses a hypothesis testing problem for comparing exponentially distributed data against a new class termed “New Better than Renewal Used in Moment Generating Function” (NBRUmgf). A measure of departure from exponentiality is constructed using the Laplace transform, followed by the development of a U-statistic-based test for the hypothesis. Additionally, a test based on the goodness of fit approach is examined as a special case. The asymptotic normality of the proposed statistic is introduced, and Pitman’s asymptotic efficiency of the two tests is computed and compared with other tests. Percentiles of the test statistics are computed for certain sample sizes in the case of complete data, and the powers of the tests are computed for popular reliability distributions. Finally, practical applications of the proposed tests are demonstrated in multiple cases. Full article
(This article belongs to the Special Issue Parametric and Nonparametric Statistics: From Theory to Applications)
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22 pages, 677 KiB  
Article
Non-Parametric Estimation of the Renewal Function for Multidimensional Random Fields
by Livasoa Andriamampionona, Victor Harison and Michel Harel
Mathematics 2024, 12(12), 1862; https://doi.org/10.3390/math12121862 - 14 Jun 2024
Viewed by 725
Abstract
This paper addresses the almost sure convergence and the asymptotic normality of an estimator of the multidimensional renewal function based on random fields. The estimator is based on a sequence of non-negative independent and identically distributed [...] Read more.
This paper addresses the almost sure convergence and the asymptotic normality of an estimator of the multidimensional renewal function based on random fields. The estimator is based on a sequence of non-negative independent and identically distributed (i.i.d.) multidimensional random fields and is expressed as infinite sums of k-folds convolutions of the empirical distribution function. It is an extension of the work from the case of the two-dimensional random fields to the case of the d-dimensional random fields where d>2. This is established by the definition of a “strict order relation”. Concrete applications are given. Full article
(This article belongs to the Special Issue Parametric and Nonparametric Statistics: From Theory to Applications)
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Figure 1

12 pages, 251 KiB  
Article
Empirical-Likelihood-Based Inference for Partially Linear Models
by Haiyan Su and Linlin Chen
Mathematics 2024, 12(1), 162; https://doi.org/10.3390/math12010162 - 4 Jan 2024
Viewed by 951
Abstract
Partially linear models find extensive application in biometrics, econometrics, social sciences, and various other fields due to their versatility in accommodating both parametric and nonparametric elements. This study aims to establish statistical inference for the parametric component effects within these models, employing a [...] Read more.
Partially linear models find extensive application in biometrics, econometrics, social sciences, and various other fields due to their versatility in accommodating both parametric and nonparametric elements. This study aims to establish statistical inference for the parametric component effects within these models, employing a nonparametric empirical likelihood approach. The proposed method involves a projection step to eliminate the nuisance nonparametric component and utilizes an empirical-likelihood-based technique, along with the Bartlett correction, to enhance the coverage probability of the confidence interval for the parameter of interest. This method demonstrates robustness in handling normally and non-normally distributed errors. The proposed empirical likelihood ratio statistic converges to a limiting chi-square distribution under certain regulations. Simulation studies demonstrate that this method provides better inference in terms of coverage probabilities compared to the conventional normal-approximation-based method. The proposed method is illustrated by analyzing the Boston housing data from a real study. Full article
(This article belongs to the Special Issue Parametric and Nonparametric Statistics: From Theory to Applications)
13 pages, 313 KiB  
Article
Asymptotic Behavior of a Nonparametric Estimator of the Renewal Function for Random Fields
by Livasoa Andriamampionona, Victor Harison and Michel Harel
Mathematics 2023, 11(19), 4048; https://doi.org/10.3390/math11194048 - 24 Sep 2023
Cited by 1 | Viewed by 777
Abstract
In this paper, we study the asymptotic normality of a nonparametric estimator of the renewal function associated with a sequence of absolutely continuous nonnegative two-dimensional random fields. We prove that this estimator is asymptotically unbiased. The asymptotic normality of this estimator is established. [...] Read more.
In this paper, we study the asymptotic normality of a nonparametric estimator of the renewal function associated with a sequence of absolutely continuous nonnegative two-dimensional random fields. We prove that this estimator is asymptotically unbiased. The asymptotic normality of this estimator is established. Full article
(This article belongs to the Special Issue Parametric and Nonparametric Statistics: From Theory to Applications)
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31 pages, 556 KiB  
Article
Change-Point Detection in the Volatility of Conditional Heteroscedastic Autoregressive Nonlinear Models
by Mohamed Salah Eddine Arrouch, Echarif Elharfaoui and Joseph Ngatchou-Wandji
Mathematics 2023, 11(18), 4018; https://doi.org/10.3390/math11184018 - 21 Sep 2023
Cited by 1 | Viewed by 1196
Abstract
This paper studies single change-point detection in the volatility of a class of parametric conditional heteroscedastic autoregressive nonlinear (CHARN) models. The conditional least-squares (CLS) estimators of the parameters are defined and are proved to be consistent. A Kolmogorov–Smirnov type-test for change-point detection is [...] Read more.
This paper studies single change-point detection in the volatility of a class of parametric conditional heteroscedastic autoregressive nonlinear (CHARN) models. The conditional least-squares (CLS) estimators of the parameters are defined and are proved to be consistent. A Kolmogorov–Smirnov type-test for change-point detection is constructed and its null distribution is provided. An estimator of the change-point location is defined. Its consistency and its limiting distribution are studied in detail. A simulation experiment is carried out to assess the performance of the results, which are compared to recent results and applied to two sets of real data. Full article
(This article belongs to the Special Issue Parametric and Nonparametric Statistics: From Theory to Applications)
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16 pages, 629 KiB  
Article
On Surprise Indices Related to Univariate Discrete and Continuous Distributions: A Survey
by Indranil Ghosh and Tamara D. H. Cooper
Mathematics 2023, 11(14), 3234; https://doi.org/10.3390/math11143234 - 23 Jul 2023
Viewed by 1320
Abstract
The notion that the occurrence of an event is surprising has been discussed in the literature without adequate details. By definition, a surprise index is an index by which how surprising an event is may be determined. Since its inception, this index has [...] Read more.
The notion that the occurrence of an event is surprising has been discussed in the literature without adequate details. By definition, a surprise index is an index by which how surprising an event is may be determined. Since its inception, this index has been evaluated for univariate discrete probability models, such as the binomial, negative binomial, and Poisson probability distributions. In this article, we derive and discuss using numerical studies, in addition to the above-mentioned probability models, surprise indices for several other univariate discrete probability models, such as the zero-truncated Poisson, geometric, Hermite, and Skellam distributions, by adopting a established strategy and using the Mathematica, version 12 software. In addition, we provide symbolical expressions for the surprise index for several univariate continuous probability models, which has not been previously discussed. For illustrative purposes, we present some possible real-life applications of this index and potential challenges to extending the notion of the surprise index to bivariate and higher dimensions, which might involve ubiquitous normalizing constants. Full article
(This article belongs to the Special Issue Parametric and Nonparametric Statistics: From Theory to Applications)
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