Robust Wald-type tests for non-homogeneous observations based on minimum density power divergence estimator

TL;DR

This paper develops robust Wald-type hypothesis tests for non-homogeneous, independent data using the minimum density power divergence estimator, ensuring robustness and applicability in generalized linear models.

Contribution

It introduces new Wald-type tests based on the minimum density power divergence estimator for non-homogeneous data, with detailed robustness analysis and applications.

Findings

The proposed tests are asymptotically robust.

They perform well in generalized linear models with normal and Poisson distributions.

The tests demonstrate improved robustness over classical methods.

Abstract

This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust minimum density power divergence estimator of the common underlying parameter. Asymptotic and theoretical robustness properties of the proposed tests have been discussed. Application to the problem of testing the general linear hypothesis in a generalized linear model with fixed-design has been considered in detail with specific illustrations for its special cases under normal and Poisson distributions.