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

Li Xing Zhu; Kai Tai Fang

doi:10.1006/aama.1994.1020

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

Li Xing Zhu
, Kai Tai Fang

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

1 Citation (Scopus)

Abstract

Suppose that x₁,…, x_m 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 y_i, 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.

Original language	English
Pages (from-to)	476-489
Number of pages	14
Journal	Advances in Applied Mathematics
Volume	15
Issue number	4
DOIs	https://doi.org/10.1006/aama.1994.1020
Publication status	Published - Dec 1994

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title = "The accurate distribution of the kolmogorov statistic with applications to bootstrap approximation",

abstract = "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.",

author = "Zhu, \{Li Xing\} and Fang, \{Kai Tai\}",

note = "The work was supported by NSF of China and a Hong Kong UPGC grant.",

year = "1994",

month = dec,

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language = "English",

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pages = "476--489",

journal = "Advances in Applied Mathematics",

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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 - https://www.scopus.com/pages/publications/43949158202

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 -

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

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