Transfer of tail information in censored regression models

• 成果类型: Article
• 署名作者: Van Keilegom, I; Akritas, MG
• 署名单位: Maastricht University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 1745-1784
• 关键词: kaplan-meier estimate; Nonparametric Regression; WEAK-CONVERGENCE; covariables; bootstrap

摘要

Consider a heteroscedastic regression model Y = m(X) + sigma(X)epsilon, where the functions m and sigma are smooth, and epsilon is independent of X. The response variable Y is subject to random censoring, but it is assumed that there exists a region of the covariate X where the censoring of Y is light. Under this condition, it is shown that the assumed nonparametric regression model can be used to transfer tail information from regions of light censoring to regions of heavy censoring. Crucial for this transfer is the estimator of the distribution of epsilon based on nonparametric regression residuals, whose weak convergence is obtained. The idea of transferrring tail information is applied to the estimation of the conditional distribution of Y given X = x with information on the upper tail borrowed from the region of light censoring, and to the estimation of the bivariate distribution P(X less than or equal to x, Y less than or equal to y) with no regions of undefined mass. The weak convergence of the two estimators is obtained. By-products of this investigation include the uniform consistency of the conditional Kaplan-Meier estimator and its derivative, the location and scale estimators and the estimators of their derivatives.