TY - JOUR

T1 - The accurate distribution of the kolmogorov statistic with applications to bootstrap approximation

AU - Zhu, Li Xing

AU - Fang, Kai Tai

N1 - The work was supported by NSF of China and a Hong Kong UPGC grant.

PY - 1994/12

Y1 - 1994/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=43949158202&partnerID=8YFLogxK

U2 - 10.1006/aama.1994.1020

DO - 10.1006/aama.1994.1020

M3 - Journal article

AN - SCOPUS:43949158202

SN - 0196-8858

VL - 15

SP - 476

EP - 489

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 4

ER -