Multivariate Rényi inaccuracy measures based on copulas: properties and application

Abstract

We propose Rényi inaccuracy measure based on multivariate copula and multivariate survival copula, respectively dubbed as multivariate cumulative copula Rényi inaccuracy measure and multivariate survival copula Rényi inaccuracy measure. Bounds of multivariate cumulative copula Rényi inaccuracy and multivariate survival copula Rényi inaccuracy measures have been obtained using Fréchet-Hoeffding bound. We discuss the comparison studies of the multivariate cumulative copula Rényi inaccuracy and multivariate survival copula Rényi inaccuracy measures based on lower orthant and upper orthant orders. We have also proposed multivariate co-copula Rényi inaccuracy and multivariate dual copula Rényi inaccuracy measures based on multivariate co-copula and dual copula. Similar properties have been explored. Further, we propose semiparametric estimator of multivariate cumulative copula Rényi 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 Rényi inaccuracy measure can be applied as a model (copula) selection criteria.