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Mathematics
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Statistics for Stochastic Processes
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Statistics for Stochastic Processes

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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 5342

Special Issue Editor

Prof. Dr. Salim Bouzebda

E-Mail Website
Guest Editor
Laboratory of Applied Mathematics of Compiègne (LMAC), Université de Technologie de Compiègne, 60200 Compiègne, France
Interests: statistics for stochastic processes; empirical process theory; U-empirical process; bootstrap; semi-/nonparametric statistical theory; functional data analysis; high-dimensional probability; statistical machine learning theory and applications

Special Issue Information

Dear Colleagues,

This Special Issue on “Statistics for Stochastic Processes” aims to publish high-quality articles on statistical inference for discrete or continuous time stochastic processes. The topic includes diffusion-type processes, point processes, random fields, Markov processes, and other time series models. This issue also accepts submissions on empirical processes and U-processes, statistical learning theory, functional data analysis, strong and weak approximations, and information theory, in addition to the abovementioned topics. The most remarkable aspect of statistical inference for stochastic processes is that it has led to interactions with other subfields of mathematics, statistics, and computer science due to the creation of powerful new tools and perspectives. Contributions that suggest potential applications of the developed theory and engineering are strongly encouraged. This Special Issue focuses heavily on methodological progress and theoretical outcomes.

Prof. Dr. Salim Bouzebda 
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

  • discrete or continuous time stochastic processes
  • diffusion-type processes
  • point processes
  • random fields
  • Markov processes
  • empirical processes and u-processes
  • statistical learning theory
  • functional data analysis

Published Papers (2 papers)

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Research

21 pages, 344 KiB  
Article
Calibration-Based Mean Estimators under Stratified Median Ranked Set Sampling
by Usman Shahzad, Ishfaq Ahmad, Fatimah Alshahrani, Ibrahim M. Almanjahie and Soofia Iftikhar
Mathematics 2023, 11(8), 1825; https://doi.org/10.3390/math11081825 - 12 Apr 2023
Cited by 5 | Viewed by 3111
Abstract
Using auxiliary information, the calibration approach modifies the original design weights to enhance the mean estimates. This paper initially proposes two families of estimators based on an adaptation of the estimators presented by recent researchers, and then, it presents a new family of [...] Read more.
Using auxiliary information, the calibration approach modifies the original design weights to enhance the mean estimates. This paper initially proposes two families of estimators based on an adaptation of the estimators presented by recent researchers, and then, it presents a new family of calibration estimators with the set of some calibration constraints under stratified median ranked set sampling (MRSS). The result has also been implemented to the situation of two-stage stratified median ranked set sampling (MRSS). To best of our knowledge, we are presenting for the first time calibration-based mean estimators under stratified MRSS, so the performance evaluation is made between adapted and proposed estimators on behalf of the simulation study with real and artificial datasets. For real-world data or applications, we use information on the body mass index (BMI) of 800 people in Turkey in 2014 as a research variable and age as an auxiliary variable. Full article
(This article belongs to the Special Issue Statistics for Stochastic Processes)
39 pages, 528 KiB  
Article
Uniform Consistency for Functional Conditional U-Statistics Using Delta-Sequences
by Salim Bouzebda, Amel Nezzal and Tarek Zari
Mathematics 2023, 11(1), 161; https://doi.org/10.3390/math11010161 - 28 Dec 2022
Cited by 10 | Viewed by 1375
Abstract
U-statistics are a fundamental class of statistics derived from modeling quantities of interest characterized by responses from multiple subjects. U-statistics make generalizations the empirical mean of a random variable X to the sum of all k-tuples of X observations. This [...] Read more.
U-statistics are a fundamental class of statistics derived from modeling quantities of interest characterized by responses from multiple subjects. U-statistics make generalizations the empirical mean of a random variable X to the sum of all k-tuples of X observations. This paper examines a setting for nonparametric statistical curve estimation based on an infinite-dimensional covariate, including Stute’s estimator as a special case. In this functional context, the class of “delta sequence estimators” is defined and discussed. The orthogonal series method and the histogram method are both included in this class. We achieve almost complete uniform convergence with the rates of these estimators under certain broad conditions. Moreover, in the same context, we show the uniform almost-complete convergence for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship, which is of its own interest. Among the potential applications are discrimination problems, metric learning and the time series prediction from the continuous set of past values. Full article
(This article belongs to the Special Issue Statistics for Stochastic Processes)
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