Robust approach for comparing two dependent normal populations through Wald-type tests based on R\'enyi's pseudodistance estimators

TL;DR

This paper introduces robust Wald-type tests based on Rényi's pseudodistance estimators for comparing two dependent normal populations, addressing the classical problem of testing correlation coefficients with improved robustness.

Contribution

It proposes a novel robust testing methodology using Rényi's pseudodistance estimators for dependent normal populations, including asymptotic properties and computational algorithms.

Findings

The tests are asymptotically robust and have bounded influence functions.

Simulation results show improved robustness over classical methods.

Real data examples confirm practical effectiveness.

Abstract

Since the two seminal papers by Fisher (1915, 1921) were published, the test under a fixed value correlation coefficient null hypothesis for the bivariate normal distribution constitutes an important statistical problem. In the framework of asymptotic robust statistics, it remains being a topic of great interest to be investigated. For this and other tests, focused on paired correlated normal random samples, R\'{e}nyi's pseudodistance estimators are proposed, their asymptotic distribution is established and an iterative algorithm is provided for their computation. From them the Wald-type test statistics are constructed for different problems of interest and their influence function is theoretically studied. For testing null correlation in different contexts, an extensive simulation study and two real data based examples support the robust properties of our proposal.