Robust Bounded Influence Tests for Independent Non-Homogeneous Observations

Several real-life experiments yield non-identically distributed data which has to be analyzed using statistical modelling techniques. Tests of any statistical hypothesis under such set-ups are generally performed using the likelihood ratio test, which is highly 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 function and are highly robust with respect to data contamination; also they have high power against any contiguous alternative and are consistent at any fixed alternative. The methodology is illustrated on the linear regression model with fixed covariates.