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

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 are discussed. Application to the problem of testing for the general linear hypothesis in a generalized linear model with a fixed-design has been considered in detail with specific illustrations for its special cases under the normal and Poisson distributions.