Advances in Statistical Modeling: Copulas, Large Sample Theory and Applications

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

Deadline for manuscript submissions: 28 February 2026 | Viewed by 1660

Special Issue Editor


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Guest Editor
Department of Mathematics, University of Mississippi, University Ave, University, MS 38677, USA
Interests: probability theory (stochastic processes, Markov and reversible Markov chains, central limit theorems, dependence coefficients and applications, copula models); statistics (kernel estimation of dependent data, Bayesian analysis, survival analysis, time series analysis, estimation methods, modeling and testing with Markov chains, large sample theory, regression analysis, ANOVA)

Special Issue Information

Dear Colleagues,

This volume is focused on recent advances in copula theory. It covers construction methods for copulas, modeling with copulas, Copula-based Markov chains, Mixing for Markov chains, measures of association, estimation problems and related large sample theories. Any applications of these topics will be considered. We are interested in models with sound theoretical novelty or that extend existing copula models to wider and more flexible families. We are particularly interested in applications involving survival analysis, time series, Bayesian analysis and regression, but any other areas are also welcome.

Dr. Martial Longla
Guest Editor

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Keywords

  • copula theory
  • mixing structure
  • large sample theory
  • copula-based Markov chains
  • new estimation methods

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Published Papers (1 paper)

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Research

22 pages, 1590 KiB  
Article
Continuous Exchangeable Markov Chains, Idempotent and 1-Dependent Copulas
by Martial Longla
Mathematics 2025, 13(12), 2034; https://doi.org/10.3390/math13122034 - 19 Jun 2025
Viewed by 1337
Abstract
New copula families are constructed based on orthogonality in L2(0,1). Subclasses of idempotent copulas with square integrable densities are derived. It is shown that these copulas generate exchangeable Markov chains that behave as independent and identically [...] Read more.
New copula families are constructed based on orthogonality in L2(0,1). Subclasses of idempotent copulas with square integrable densities are derived. It is shown that these copulas generate exchangeable Markov chains that behave as independent and identically distributed random variables conditionally on the initial variable. We prove that the extracted family of copulas is the only set of symmetric idempotent copulas with square integrable densities. We extend these copula families to asymmetric copulas with square integrable densities having special dependence properties. One of our extensions includes the Farlie–Gumbel–Morgenstern (FGM) copula family. The mixing properties of Markov chains generated by these copulas are established. The Spearman’s correlation coefficient ρS is provided for each of these copula families. Some graphs are also provided to illustrate the properties of the copula densities. Full article
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