On the Robustness of LM, LR, and W Tests in Regression Models

Abstract

In this paper we show that, in the small sample case, while the LR test is robust, the LM and W tests are not robust when the errors are Student t. For the large sample, however, all three tests are found to be robust. A variation of the W test is also considered and it turns out to be nonrobust. The implications of assuming the errors to be distributed as multivariate Student t, rather than multivariate normal, are also discussed. It is found that not all of Evans and Savin's [4] results carry through when the errors are Student t.