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 -