On the Pitman Efficiency of One-sided Kolmogorov and Smirnov Tests for Normal Alternatives

Abstract

Lower bounds for the Pitman efficiency of the one-sided Kolmogorov test for all normal alternatives and for the Smirnov test for normal shift alternatives are obtained. In the one-sample case this does not fall below 36 per cent at the usual levels of significance and power. In the two-sample case the lower bound depends on the ratio of the two sample sizes and does not fall below 36 per cent when the ratio is larger than 40. We assume that the results of [1] are known.