Minimum-distance statistics for the selection of an asymmetric copula in Khoudraji's class of models

Jean François Quessy, Othmane Kortbi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The modeling of bivariate dependence is usually accomplished with symmetric copula models. However, many examples of datasets show that this hypothesis of symmetry may fail to hold, so there is a need for inferential methods using asymmetric dependence structures. In this paper, useful tools for modeling non-exchangeable dependence structures are developed under a broad class of asymmetric copulas introduced by Khoudraji (1995). Special attention is given to the testing of the composite hypothesis that the underlying copula of a population belongs to this general class of models. The problem of selecting a specific Khoudraji-type copula via goodness-of-fit testing is considered as well, hence providing a complete set of tools for inference when facing bivariate data exhibiting an asymmetric dependence structure. Monte Carlo simulations show that the newly introduced methodologies work well in small and moderate sample sizes. Their usefulness for copula modeling is illustrated on data sets exhibiting patterns of asymmetric dependence.

Original languageEnglish
Pages (from-to)177-204
Number of pages28
JournalStatistica Sinica
Volume26
Issue number1
DOIs
Publication statusPublished - Jan 2016
Externally publishedYes

Keywords

  • Empirical copula process
  • Multiplier bootstrap
  • Shape hypothesis

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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