On the Asymptotic Efficiency of the Kolmogorov-Smirnov Test
Jack Capon · Journal of the American Statistical Association · 1965
The Kolmogorov-Smirnov test is important in nonparametric statistical inference. The limiting distribution of the Kolmogorov-Smirnov statistic under the null hypothesis is well known and has been derived by several different methods. The limiting distribution of this statistic under the alternative hypothesis is unknown so that it is not possible, in general, to compute the power of the Kolmogorov-Smirnov test. It is possible, however, to compute a lower bound for the power of this test. This result is used to calculate a lower bound for the asymptotic efficiency of the Kolmogorov-Smirnov test relative to the optimum likelihood ratio test. Applications are given to Cauchy, exponential and normal populations. In addition, a lower bound for the asymptotic efficiency of the Kolmogorov-Smirnov test relative to the t-test is computed for translation alternatives.