Multivariate R\'enyi inaccuracy measures based on copulas: properties and application

TL;DR

This paper introduces new multivariate Rénnyi inaccuracy measures based on copulas, explores their properties, bounds, and comparisons, and demonstrates their application in model selection through simulations and real data analysis.

Contribution

It proposes novel multivariate Rénnyi inaccuracy measures based on copulas, develops their properties, bounds, estimators, and applies them to model selection.

Findings

Derived bounds using Fréchet-Hoeffding bounds.

Developed a semiparametric estimator with simulation validation.

Applied measures effectively for copula model selection.

Abstract

We propose R\'enyi inaccuracy measure based on multivariate copula and multivariate survival copula, respectively dubbed as multivariate cumulative copula R\'enyi inaccuracy measure and multivariate survival copula R\'enyi inaccuracy measure. Bounds of multivariate cumulative copula R\'enyi inaccuracy and multivariate survival copula R\'enyi inaccuracy measures have been obtained using Fr\'echet-Hoeffding bound. We discuss the comparison studies of the multivariate cumulative copula R\'enyi inaccuracy and multivariate survival copula R\'enyi inaccuracy measures based on lower orthant and upper orthant orders. We have also proposed multivariate co-copula R\'enyi inaccuracy and multivariate dual copula R\'enyi inaccuracy measures based on multivariate co-copula and dual copula. Similar properties have been explored. Further, we propose semiparametric estimator of multivariate cumulative copula R\'enyi inaccuracy measure. A simulation study is performed to compute standard deviation, absolute bias and mean squared error of the proposed estimator. Finally, a data set is considered to show that the multivariate cumulative copula R\'enyi inaccuracy measure can be applied as a model (copula) selection criteria.