Robust Testing Procedures in Heteroscedastic Linear Models

There exist many studies which treat the robust tests in homoscedastic linear models. However, the robust testing procedure in heteroscedastic linear models has not been examined. In this article, three classes of testing procedures for testing subhypothesis in heteroscedastic linear models are developed. These are Wald-type, score-type, and drop-in dispersion tests. The asymptotic distributions of these tests are obtained under the null hypothesis and contiguous alternatives. For a robustness criterion, the maximum asymptotic bias of the level of the test for distributions in a shrinking contamination neighborhood is used and the most-efficient robust test is derived. Finally, the performance of these tests in small sample is studied by Monte Carlo simulation.