Suppose that x1,…, xm are i.i.d. variables with distribution F(·). When F(·) is continuous, the accurate distribution of the Kolmogorov statistic was obtained by Zhang. In this paper, a discrete distribution F(·) which masses value 1/n at each point yi, i = 1,…, n is considered, the obtained accurate distribution of the Kolmogorov, statistic has the same form as that of Zhang′s. By this result, the bootstrap approximation of the distribution of the Kolmogorov statistic is investigated, and the √n -asymptotic rate is obtained.
Scopus Subject Areas
- Applied Mathematics