Asymptotic Efficiency of the Two Sample Kolmogorov-Smirnov Test

A simple derivation of asymptotic efficiency for the two sample 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 α go to zero while the type II error goes to β, 0 < β < 1. For unimodal 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 2/π for normal location alternatives and (πe)−1 for normal scale alternatives.