ASYMPTOTIC EFFICIENCY OF THE KOLMOGOROV - SMIRNOV TEST
WISCONSIN UNIV-MADISON DEPT OF STATISTICS
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A simple derivation of asymptotic efficiency for the Kolmogorov - Smirnov statistic is given and evaluated for normal location and normal scale alternatives. Using equal samples to simplify the derivation, the limiting efficiency is obtained by letting the type I error alpha go to zero while the type II error goes to beta, 0 beta 1. For symmetric location alternatives, the efficiency is the same as that obtained for the Mood and Brown median test. Limits of relative efficiencies for alternatives which approach the null hypothesis are 2pi for normal location alternatives and 1piE for normal scale alternatives.
- Statistics and Probability