Application of Bootstrap Method in Kolmogorov-Smirnov Test

The maximum difference between the empirical distribution function and the theoretical distribution function is random in Kolmogorov-Smirnov(K-S) test. The distribution of this maximum difference, including mean and deviation, is studied based on bootstrap method in this paper. Firstly, the simulated samples are randomly re-sampled from the original finite observed samples. Then the maximum difference is obtained from this simulated samples by performing K-S test. A series of maximum difference can be obtained by repeating the above process. Finally, the optimal model is selected from the model whose maximum difference is very near to the mean difference of the whole simulated samples. The experimental results show that by using bootstrap method, not only the optimal model can be estimated but also the confidence of the K-S test conclusion can be given even in case of limit number of original observed samples.