Robustness Properties of the F-Test and Best Linear Unbiased Estimators in Linear Models.

Abstract

Abstract : Document considers a linear model Y = X beta + sigma epsilon, E(epsilon) = O, E(epsilon prime) = I sub n with beta, sigma unknown. For the problem of testing the linear hypothesis C beta = sigma im(C prime) a subset of im(X prime), Ghosh and Sinha (1980) proved that the properties of the usual F-test being LRT and UMPI (under a suitable group a transformations) remain valid for specific non-normal families. In this paper it is shown that both criterion and inference robustness of the F-test hold under the assumption epsilon about q(epsilon prime), q convex and isotonic. This result is similar to a robustness property of Hotelling's T squared-test proved by Kariya (1981). Finally it is proved that the Best Linear Unbiased Estimator (BLUE) of any estimable function beta is more concentrated around C beta than any other unbiased estimator of C beta under the assumption that epsilon is spherically distributed.