A simulation study of semiparametric estimation in copula models based on minimum Alpha-Divergence

TL;DR

This paper introduces two novel semiparametric copula parameter estimation methods based on minimum Alpha-Divergence, demonstrating superior performance in small samples and weak dependencies through simulation and real data application.

Contribution

It proposes new semiparametric estimation techniques using Alpha-Divergence, extending beyond traditional maximum pseudo-likelihood methods.

Findings

Minimum Pseudo Hellinger Distance performs well with small samples.

Methods outperform MPL in weak dependency scenarios.

Application to hydrology data validates practical usefulness.

Abstract

The purpose of this paper is to introduce two semiparametric methods for the estimation of copula parameter. These methods are based on minimum Alpha-Divergence between a non-parametric estimation of copula density using local likelihood probit transformation method and a true copula density function. A Monte Carlo study is performed to measure the performance of these methods based on Hellinger distance and Neyman divergence as special cases of Alpha-Divergence. Simulation results are compared to the Maximum Pseudo-Likelihood (MPL) estimation as a conventional estimation method in well-known bivariate copula models. These results show that the proposed method based on Minimum Pseudo Hellinger Distance estimation has a good performance in small sample size and weak dependency situations. The parameter estimation methods are applied to a real data set in Hydrology.