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研究生:劉宜雅
研究生(外文):Liu Yi -ya
論文名稱:左截與右設限下,雙變數在存活函數之無母數估計
論文名稱(外文):Nonparametric estimation of the bivariate survival function whenboth components are subject to left-truncation and right-censoring
指導教授:沈葆聖沈葆聖引用關係
指導教授(外文):Shen Pao-sheng
口試委員:黃連成戴政
口試日期:2012-07-03
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:2012
畢業學年度:100
語文別:英文
論文頁數:15
外文關鍵詞:Bivariate distributionTruncationCensoring
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  • 下載下載:9
  • 收藏至我的研究室書目清單書目收藏:0
我們考慮估計雙變數存活函數時,這兩個成分左截斷,右設限。沈和楊(2008)認為
兩個類型的Dabrowska和Campbell-Foldes的一般估計。他們的方法需要繁瑣的計算。
我們提出了一個替代的估計,這很容易實現,不需要遞迴。估計的一致性被建立。模擬結果表明,該估計優於沈和楊(2008)的估計

We consider estimating the bivariate survival function when both components
are subject to left truncation and right censoring. Shen and Yan (2008) consider
two types of estimators as generalizations of the Dabrowska and Campbell and
Foldes estimators. Their method requires tedious computation. In this note, we
propose an alternative estimator, which is easy to implement and does not require
iteration. The consistency of the proposed estimators is established. Simulation
results indicate that the proposed estimator outperforms the estimators of Shen
and Yan (2008)
con

1.Introduction 1
Example 1.1                      1
Example 1.2 1

2. The Proposed Estimators 7

3. Simulation Studies 9
3.1 General Case 10
3.2 Special Case 11

4. Conclusion and Discussion 12

References 12

Dabrowska, D. M. (1988), Kaplan-Meier estimate on the plane. Ann. Statist., 18,
1475-1489.
Dabrowska, D. M. (1989), Kaplan-Meier estimate on the plane: weak convergence,
LIL, and the bootstrap, J. Multivariate Anal. 29, 308-325
Gill, R. D., van der Laan, M. J., and Wellner J. A. (1995), Inecient estimators
of the bivariate survival function for three models. Annales de l'Institut Henri
Poincare. Section B, Probabilites et statistiques 31, 547-597.
Campbell, G. and Foldes, A. (1982). Large sample properties of nonparametric
statistical inference. In Nonparametric Statistical Inference (B. V. Gnredenko, M.
L. Puri, and I. Vineze, eds.). Amsterdam:North-Holland. 103-122.
Gijbels, I. and Gurler, U
. (1996), 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.
Gijbels, I. and Gurler, U
. (1998), Covariance function of a bivariate distribution
function estimator for left truncated and right censored data. Statistica Sinica, 8
1219-1232.
Gurler, U
. (1996), Bivariate estimation with right truncated data. J. Amer. Statist.
Assoc., 91, 1152-1165.
Gurler, U
. (1997), Bivariate distribution and hazard functions when a component
is randomly truncated. J. Multivariate Anal., 60, 20-47.
Prentice, R. L. and Cai, J. (1992), Covariance and survivor function estimation
using censored multivariate failure time data. Biometrika 79, 495-512.
Pruitt, R. C. (1991), Strong consistency of self-consistent estimators:general theory
and an application to bivariate survival analysis, Technical Report nr. 543,
University of Minnesota.
Pruitt, R. C. (1993), Small sample comparisons of six bivariate survival curve estimators.
J. Statist. Comput. Simul., 45, 147-167.
Shen, P.-S. (2006), An inverse-probability-weighted approach to estimation of the
bivariate survival function under left-truncation and right-censoring. Journal of
Statistical Planning and Inference, 136, 4365-4384.
Shen, P.-S. and Yan, Y. F. (2008). Nonparametric estimation of the bivariate
survival function with left-truncated and right-censored data. Journal of Statistical
Planning and Inference, Vol. 138, pp. 4041-4054.
van der Laan, M. J. (1996a), Nonparametric estimation of the bivariate survival
function with truncated data. J. Multivariate Anal. 58, 107-131.
van der Laan, M. J. (1996b), Ecient estimation in the bivariate censoring model
and repairing NPMLE. Ann. Statist., 24, 596-627.
van der Laan, M. J. (1997), Nonparametric estimators of the bivariate survival
function under random censoring. Statist. Nederland., 51, 178-200.
van der Vaart, and Wellner (2000), Weak convergence and Empirical process with
application to Statistics. Springer
Wang, M. C. (1991), Nonparametric estimation from cross-sectional survival data.
Journal of the American Statistic Association 86, 130-143.
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