STRONG EMBEDDING OF PRODUCT-LIMIT ESTIMATOR OF BIVARIATE SURVIVAL DISTRIBUTION FUNCTION UNDER RANDOM CENSORSHIP

数学物理学报(英文版) ›› 1995, Vol. 15 ›› Issue (S1): 123-132.

STRONG EMBEDDING OF PRODUCT-LIMIT ESTIMATOR OF BIVARIATE SURVIVAL DISTRIBUTION FUNCTION UNDER RANDOM CENSORSHIP

王启华

Department of Probability and statistics, Peking University, Beijing 100871, China

收稿日期:1993-03-09 出版日期:1995-12-31 发布日期:1995-12-31
基金资助:
Supported by the doctoral programme scientific foundation and NSFC.

STRONG EMBEDDING OF PRODUCT-LIMIT ESTIMATOR OF BIVARIATE SURVIVAL DISTRIBUTION FUNCTION UNDER RANDOM CENSORSHIP

Wang Qihua

Department of Probability and statistics, Peking University, Beijing 100871, China

Received:1993-03-09 Online:1995-12-31 Published:1995-12-31
Supported by:
Supported by the doctoral programme scientific foundation and NSFC.

摘要/Abstract

摘要： Let (X_i⁰,Y_i⁰), 1 ≤ i ≤ n be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t)=P(X⁰ > s,Y⁰ > t). Let S_n(s,t) be the product-limit estimator of S(s,t) suggested by Campbell and Földes (1980). In this paper it is shown that under some conditions a sequence of Gaussian processes G_n(s,t) can be constructed such that
sup_0T^0S|n^(1)/2[S_n(s,t)-S(s,t)]-G_n(s,t)|=O(n^-(1)/2 log²n) a. s.,for S,T which together satisfy a certain condition.

关键词: Strong Embedding, Product-Limit Estimator, Survival Distribution

Abstract: Let (X_i⁰,Y_i⁰), 1 ≤ i ≤ n be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t)=P(X⁰ > s,Y⁰ > t). Let S_n(s,t) be the product-limit estimator of S(s,t) suggested by Campbell and Földes (1980). In this paper it is shown that under some conditions a sequence of Gaussian processes G_n(s,t) can be constructed such that
sup_0T^0S|n^(1)/2[S_n(s,t)-S(s,t)]-G_n(s,t)|=O(n^-(1)/2 log²n) a. s.,for S,T which together satisfy a certain condition.

Key words: Strong Embedding, Product-Limit Estimator, Survival Distribution

王启华. STRONG EMBEDDING OF PRODUCT-LIMIT ESTIMATOR OF BIVARIATE SURVIVAL DISTRIBUTION FUNCTION UNDER RANDOM CENSORSHIP[J]. 数学物理学报(英文版), 1995, 15(S1): 123-132.

Wang Qihua. STRONG EMBEDDING OF PRODUCT-LIMIT ESTIMATOR OF BIVARIATE SURVIVAL DISTRIBUTION FUNCTION UNDER RANDOM CENSORSHIP[J]. Acta mathematica scientia,Series B, 1995, 15(S1): 123-132.

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[2]	孙六权, 郑忠国. STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR ON INCREASING SETS FOR TRUNCATED \|AND CENSORED DATA[J]. 数学物理学报(英文版), 1999, 19(3): 251-260.
[3]	周勇. A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA[J]. 数学物理学报(英文版), 1996, 16(2): 170-180.

STRONG EMBEDDING OF PRODUCT-LIMIT ESTIMATOR OF BIVARIATE SURVIVAL DISTRIBUTION FUNCTION UNDER RANDOM CENSORSHIP

STRONG EMBEDDING OF PRODUCT-LIMIT ESTIMATOR OF BIVARIATE SURVIVAL DISTRIBUTION FUNCTION UNDER RANDOM CENSORSHIP

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