BAHADUR EFFICIENCY AND ROBUSTNESS OF STUDENTIZED SCORE TESTS

We derive the exact Bahadur slopes of studentized score tests for a si mple null hypothesis in a one-parameter family of distributions. The S tudent's t-test is included as a special case for which a recent resul t of Rukhin (1993, Sankhya Ser. A, 55, 159-163) was improved upon. It is shown that locally optimal Bahadur efficiency for one-sample locati on models with a known or estimated scale parameter is attained within the class of studentized score tests. The studentized test has an asy mptotic null distribution free of the scale parameter, and the optimal ity of likelihood scores does not depend on the existence of a moment generating function. We also consider the influence function and break down point of such tests as part of our robustness investigation. The influence of any studentized score test is bounded from above, indicat ing certain degree of robustness of validity, but a bounded score func tion is needed to cap the influence from below and to ensure a high po wer breakdown point. We find that the standard Huber-type score tests are not only locally minimax in Bahadur efficiency, but also very comp etitive in global efficiency at a variety of location models.