Asymptotic distribution of the Kaplan-Meier U-statistics

被引:8
作者
Bose, A [1 ]
Sen, A
机构
[1] Indian Stat Inst, Kolkata 700035, W Bengal, India
[2] Univ Hyderabad, Hyderabad 500134, Andhra Pradesh, India
关键词
random censoring; Kaplan-Meier integral; U-statistics; central limit theorem; law of iterated logarithm; degenerate U-statistics; double Wiener integral;
D O I
10.1006/jmva.2001.2039
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Consider the Kaplan-Meier estimate of the distribution function for right randomly censored data. We show that a U-statistic defined via this estimate is asymptotically normal. Under a condition of degeneracy, different from the degeneracy condition in uncensored models, it has an asymptotic nonnormal distribution. (C) 2002 Elsevier Science (USA).
引用
收藏
页码:84 / 123
页数:40
相关论文
共 16 条
[1]   The strong law of large numbers for Kaplan-Meier U-statistics [J].
Bose, A ;
Sen, A .
JOURNAL OF THEORETICAL PROBABILITY, 1999, 12 (01) :181-200
[2]  
Bose A, 1998, ANN STAT, V26, P771
[3]  
BOSE A, 1996, 2896 IND STAT I STAT
[4]  
BOSE A, 1997, 1697 IND STAT I STAT
[5]   SYMMETRIC STATISTICS, POISSON POINT-PROCESSES, AND MULTIPLE WIENER INTEGRALS [J].
DYNKIN, EB ;
MANDELBAUM, A .
ANNALS OF STATISTICS, 1983, 11 (03) :739-745
[6]   ALMOST SURE ASYMPTOTIC REPRESENTATION FOR A CLASS OF FUNCTIONALS OF THE KAPLAN-MEIER ESTIMATOR [J].
GIJBELS, I ;
VERAVERBEKE, N .
ANNALS OF STATISTICS, 1991, 19 (03) :1457-1470
[7]  
KOUL HL, 1982, IMS LECT NOTES MONOG, V2, P189
[8]   CRAMER VON MISES STATISTIC FOR RANDOMLY CENSORED DATA [J].
KOZIOL, JA ;
GREEN, SB .
BIOMETRIKA, 1976, 63 (03) :465-474
[9]  
LIGHT WA, 1985, LECT NOTES MATH, V1169, pR5
[10]  
PARTHASARTHY KR, 1992, INTRO QUANTUM STOCHA, P20403