# 臺灣博碩士論文加值系統

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 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-Foldes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 componentsare subject to left truncation and right censoring. Shen and Yan (2008) considertwo types of estimators as generalizations of the Dabrowska and Campbell andFoldes estimators. Their method requires tedious computation. In this note, wepropose an alternative estimator, which is easy to implement and does not requireiteration. The consistency of the proposed estimators is established. Simulationresults indicate that the proposed estimator outperforms the estimators of Shenand Yan (2008)
 con1.Introduction 1Example 1.1 　　　　　　　　　　　　　　　　　　　　 1Example 1.2 12. The Proposed Estimators 73. Simulation Studies 93.1 General Case 103.2 Special Case 114. Conclusion and Discussion 12References 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, 308-325Gill, R. D., van der Laan, M. J., and Wellner J. A. (1995), Inecient estimatorsof the bivariate survival function for three models. Annales de l'Institut HenriPoincare. Section B, Probabilites et statistiques 31, 547-597.Campbell, G. and Foldes, A. (1982). Large sample properties of nonparametricstatistical inference. In Nonparametric Statistical Inference (B. V. Gnredenko, M.L. Puri, and I. Vineze, eds.). Amsterdam:North-Holland. 103-122.Gijbels, I. and Gurler, U. (1996), Covariance function of a bivariate distributionfunction estimator for left truncated and right censored data. Discussion paperNO. 9703, 1996, Institute of Statistics, Catholic University of Louvain, Louvain-la-Neuve, Belgium.Gijbels, I. and Gurler, U. (1998), Covariance function of a bivariate distributionfunction estimator for left truncated and right censored data. Statistica Sinica, 81219-1232.Gurler, U. (1996), Bivariate estimation with right truncated data. J. Amer. Statist.Assoc., 91, 1152-1165.Gurler, U. (1997), Bivariate distribution and hazard functions when a componentis randomly truncated. J. Multivariate Anal., 60, 20-47.Prentice, R. L. and Cai, J. (1992), Covariance and survivor function estimationusing censored multivariate failure time data. Biometrika 79, 495-512.Pruitt, R. C. (1991), Strong consistency of self-consistent estimators:general theoryand 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 thebivariate survival function under left-truncation and right-censoring. Journal ofStatistical Planning and Inference, 136, 4365-4384.Shen, P.-S. and Yan, Y. F. (2008). Nonparametric estimation of the bivariatesurvival function with left-truncated and right-censored data. Journal of StatisticalPlanning and Inference, Vol. 138, pp. 4041-4054.van der Laan, M. J. (1996a), Nonparametric estimation of the bivariate survivalfunction with truncated data. J. Multivariate Anal. 58, 107-131.van der Laan, M. J. (1996b), Ecient estimation in the bivariate censoring modeland repairing NPMLE. Ann. Statist., 24, 596-627.van der Laan, M. J. (1997), Nonparametric estimators of the bivariate survivalfunction under random censoring. Statist. Nederland., 51, 178-200.van der Vaart, and Wellner (2000), Weak convergence and Empirical process withapplication to Statistics. SpringerWang, M. C. (1991), Nonparametric estimation from cross-sectional survival data.Journal of the American Statistic Association 86, 130-143.
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 1 截切連續事件資料之統計分析 2 不同抽樣限制下條件存活函數之無母數平滑估計 3 申訴理賠時間與醫療成本的二元分配函數 4 左截取及右設限下續發性時間之無母數估計 5 左截取右設限下雙變數存活函數之無母數估計 6 左截取及右設限下雙變數存活函數的無母數估計:逆加權法 7 左截取右設限下的雙變數估計 8 左截取與右設限資料的雙變數無母數估計 9 左截取右設限之雙變數存活函數之逆加權估計 10 設限與截斷資料Weibull模式之研究

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