Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series A, Pt. 3, pp. 418--439

ON THE RELETIONSHIP BETWEEN POWER OFA TEST AND SHAPE OF ITS CRITICAL REGION

By

DARYL TINGLEY and MAUREEN TINGLEY, University of New Brunswick

SUMMARY.  With the Neyman-Pearson Lemma as yard-stick for comparisons, the relationship is investigated between test power and shape of critical region, as test size approaches to zero. Measuretheoretic definitions are used to quantify the notion of similar versus dissimilar critical regions. Results are obtained for two extremes of limiting power: power approaching to that of Neyman-Pearson, and power negligible when compared with Neyman-Pearson, as test size decreases.
        Examples illustrate that small test sizes are not practical when sample estimates replaces values of nuisance parameters.

AMS subject classification.  62F03, 62A10, 62F05.

Key words and phrases. Asymptotic results, critical regions, Neyman-Pearson, power.

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This article in Mathematical Reviews.