Statistica Sinica 28 (2018), 1133-1155

ROBUST BOUNDED INFLUENCE TESTS FOR

INDEPENDENT NON-HOMOGENEOUS OBSERVATIONS

Abhik Ghosh and Ayanendranath Basu

Indian Statistical Institute

Abstract: Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model misspecification. In this paper, we consider the set-up of non-identically but independently distributed observations and develop a general class of test statistics for testing parametric hypothesis based on the density power divergence. The proposed tests have bounded influence functions, are highly robust with respect to data contamination, have high power against contiguous alternatives, and are consistent at any fixed alternative. The methodology is illustrated by the simple and generalized linear regression models with fixed covariates.

Key words and phrases: Generalized linear model, influence function, linear regression, non-homogeneous observation, robust testing of hypothesis.