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研究生:林秀燕
研究生(外文):Hsiu-Yen Lin
論文名稱:左截取與右設限資料的雙變數無母數估計
論文名稱(外文):Nonparametric Bivariate Estimation with Left-Truncated and Right-Censored Data
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:2004
畢業學年度:92
語文別:英文
中文關鍵詞:雙變數分配截取設限
外文關鍵詞:bivariate distributiontruncationcensoring
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存活分析資料中的雙變數估計再近年來逐漸受到注意.在這篇論文中,我們考慮了雙變數觀察資料的情況,其中一個變數是左截取右設限,另一個變數則只有右設限.我們考慮了兩種無母數的估計方法.第一種是Satten and Datta 在2001年所提出的inverse-probability-weighted average,第二種則是Dabrowska在1988年所提的估計,並利用電腦模擬對其做比較.
Bavariate estimation with survival data has received considerable attention recently. In this paper we consider the situation of bivariate observations where one of the components is subject to left and right censoring and the other is subject to the right censoring only. Two types of nonparametric estimators are considered. The first one is the form of inverse-probability-weighted average (Satten and Datta (2001)). The second one is the generalization of Dabrowska’s (1988) estimator. The two types of estimators are then compared based on their empirical performances.
Abstract -----------------------------------------2
1 Introduction------------------------------------3
2 Inverse-Probability-Weighted Estimators---------5
3 Dabrowska''s Estimator--------------------------10
4 Simulation Results-----------------------------13
References---------------------------------------16
S-Plus Simulation Program------------------------17
Dabrowska, D. M. Kaplan-Meier estimate on the plane. The Annals of Statistics, 1988, 18, 308-325.
Gijbels, I. and Gürler, Ü. Covariance function of a bivariate distribution function estimator for left truncated and right censored data. Discussion paper NO. 9703, 1996,
Institute of Statistics, Catholic University of Louvain, Louvain-la-Neuve, Belgium.
Kaplan, E. L.; Meier, P. Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc., 1958, 53, 457-481.
Lai, T. L. and Ying, Z. Estimation a distribution function with truncated and censored data. Ann. Statist., 1991 19, No. 1, 417-442.
Prentice, R. L. and Cai, J. Convariance and survivor function estimation using censored multivariate failure time data. Biometrika, 1992, 79, 495-512.
Shen P-S. The product-limit estimate as an inverse-probability-weighted average. Communi. in Statist., Part A- Theory and Methods, 2003, 32, 1119-1133.
Satten, G. A. and Datta S. The Kaplan-Meier estimator as an inverse-probability-of —censoring weighted average. Amer. Statist. Ass., 2001, 55, 207-210.
Tsai, W.-Y., Jewell, N. P. and Wang, M.-C. A note on the product-limit estimator 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. Product-limit estimates: a generalized maximum likelihood study. Communi. in Statist., Part A- Theory and Methods, 1987, 6, 3117-3132.
Woodroofe, M. Estimating a distribution function with truncated data. 1985, The Annals of Statistics, 13, 163-167.
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