Fixed design nonparametric regression with truncated and censored data

被引：0
作者：
Liu-quan Sun
机构：
[1] Academy of Mathematics and System Sciences, Chinese Academy of Sciences
来源：
Acta Mathematicae Applicatae Sinica | 2003年 / 19卷 / 2期
基金：
中国国家自然科学基金;
关键词：
Asymptotic representation; Fixed design; Modulus of continuity; Nonparametric regression; Truncated and censored data;
D O I：
10.1007/s10255-003-0098-y
中图分类号：
学科分类号：
摘要：
In this paper we consider a fixed design model in which the observations are subject to left truncation and right censoring. A generalized product-limit estimator for the conditional distribution at a given covariate value is proposed, and an almost sure asymptotic representation of this estimator is established. We also obtain the rate of uniform consistency, weak convergence and a modulus of continuity for this estimator. Applications include trimmed mean and quantile function estimators. © Springer-Verlag 2003.
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页码：229 / 238
页数：9
相关论文
共 14 条
  • [1] Beran R., Nonparametric regression with randomly censored data, (1981)
  • [2] Billingsley P., Convergence of probability measures, (1968)
  • [3] Dabrowska D.M., Variable bandwidth conditional Kaplan-Meier estimate, Ann. Statist, 17, pp. 1157-1167, (1992)
  • [4] Gijbels I., Wang J.L., Strong representations of the survival function estimator for truncated and censored data with applications, J. Multivariate Anal, 47, pp. 210-229, (1993)
  • [5] Gonzalez-Manteiga W., Cadarso-Suarez C., Asymptotic properties of a generalized Kaplan-Meier estimator with some applications, J. Nonparametric Statistics, 4, pp. 65-78, (1994)
  • [6] Gross S.T., Lai T.L., Nonparametric estimation and regression analysis with left-truncated and right-censored data, J. Amer. Statist. Assoc, 91, pp. 1166-1180, (1996)
  • [7] Lai T.L., Ying Z., Estimating a distribution with truncated and censored data, Ann. Statist, 19, pp. 417-442, (1991)
  • [8] Lo S.H., Singh K., The product-limit estimator and the bootstrap: Some asymptotic representations, Probab. Theory Related Fields, 71, pp. 455-465, (1986)
  • [9] Nadaraya I.E., On estimating regression, Theory Probab. Appl, 9, pp. 141-142, (1964)
  • [10] Sun L., Bandwidth choice for hazard rate estimators from left truncated and right censored data, Statist. Probab. Lett, 36, pp. 101-114, (1997)
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