Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 1 , pp. 118--127

COMPARISON OF TESTS IN THEIR ORIGINAL FORMS

By

RAHUL MUKERJEE, Indian Institute of Management, Calcutta

SUMMARY. In the multiparameter setting, we consider a very large class of tests which includes the likelihood ratio, Rao’s and Wald’s tests. The tests are considered in their original forms, that is, we do not correct them for local unbiasedness as done in several other recent works. In this set-up a second order optimality property for the likelihood ratio test in terms of local maximinity and a third order optimality property for Rao’s test in terms of local ‘average’ power are proved. A numerical study is presented to demonstrate that the findings may be valid even when the sample size is not too large.

AMS (1980) subject classification. 62E20.

Key words and phrases. Average power, contiguous alternatives, likelihood ratio test, local maximinity, Rao's test, Wald's test.

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