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研究生:陳冠廷
研究生(外文):Guan-Ting Chen
論文名稱:隨機截取及右設限下的連乘估計值及其積分的強收斂一致性
論文名稱(外文):On the Strong Convergence Of The Product-Limit Estimator And Its integrals Under Random Truncation And Right Censoring
指導教授:沈葆聖沈葆聖引用關係
指導教授(外文):Pao-Sheng Shen
學位類別:碩士
校院名稱:東海大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:21
中文關鍵詞:左截取右設限強均勻一致性
外文關鍵詞:left truncationright censoring uniform strong consistent
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In this note,using inverse-probability-weighted(IPW)estimators of F,G and Q,we show that the product limit estimator Fn is uniformly strong consistent. Moreover we show integral converges almost surely.
ABSTRACT
1.Introduction......................................................3
2.Inverse-probability-weighted(IPW)Estimtors........................6
2.1 Notations......................................................6
2.2 The NPMLE of F,Gand Q..........................................7
3.The Equivalence of three truncation probability..................11
4.Strong Law Large Numbers.........................................13
5.Appendices.......................................................17
6.Reference........................................................18
Gross, S. T. and Lai, T. L.Bootstrap methods for truncated data and censored data.Statist. Sinica,1996a,6,509-530.

Gross, S. T. and Lai, T. L.Nonparametric estimation and regression analysis with left-truncated andright-censored data.J. Amer. Statist. Ass.,1996b,91,1166-1180.

He, S. and Yang, G. L.Estimation of the truncation probability in the random truncation model.Ann. Statist.,1998a,26,1011-1027.

He, S. and Yang, G. L.The strong law under random truncation.Ann. Statist.,1998b,26,992-1010.

Hyde, J. Testing survival under right censoring and left truncation.
Biometrika.,1977,64,225-230.

Hyde, J. Survival analysis with incomplete observations. In Biostatistics Casebook, R. G. Miller, B. Efron, B. W. Brown, and L. E. Moses, eds,New York: John Wiley and Sons, 1980, pp. 31-46.

Satten, G. A. and Datta S.The Kaplan-Meier estimator as an inverse-probability-of-censoring weighted average.Amer. Statist.,2001,55,207-210.

Shen, P.-S. The product-limit estimates as an inverse-probability-weighted average.Communi. in Statist., Part A- Theory and Methods,
2003,32,1119-1133.

Shen, P.-S. Estimation of the truncation probability with left-truncated and right-censored data (under revision).

Tsai, W.-Y., Jewell, N. P. and Wang, M.-C.A note on the product-limit estimate under right censoring and left truncation. Biometrika,1987,74,883-886.

Van der Laan, M. J.Nonparametric estimation of the bivariate survival function with truncated data.J. Multivariate Anal.,1996,58,107-131.

Wang, M.-C.; Jewell, N. P.; Tsai, W.-Y. Asymptotic properties
of the product-limit estimate under random truncation. Ann.Statist.,
1986,14,1597-1605.

Wang, M.-C.Product-limit estimates: a generalized maximum likelihood study.Communi. in Statist., Part A- Theory and Methods,1987,6,3117-3132.

Wang, M.-C.Nonparametric estimation from cross-sectional survival data.J. Amer. Statist. Ass.,1991,86,130-143.

Woodroofe, M. Estimating a distribution function with truncated data.Ann. Statist.,1985,13,163-167.
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