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October 1999 Transfer of tail information in censored regression models
Ingrid Van Keilegom, Michael G. Akritas
Ann. Statist. 27(5): 1745-1784 (October 1999). DOI: 10.1214/aos/1017939150

Abstract

Consider a heteroscedastic regression model $Y = m(X) + \sigma(X)\varepsilon$, where the functions $m$ and $\sigma$ are “smooth,” and $\varepsilon$ 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 $\varepsilon$ 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 $P(X \leq x, Y \leq y)$ 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.

Citation

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Ingrid Van Keilegom. Michael G. Akritas. "Transfer of tail information in censored regression models." Ann. Statist. 27 (5) 1745 - 1784, October 1999. https://doi.org/10.1214/aos/1017939150

Information

Published: October 1999
First available in Project Euclid: 23 September 2004

zbMATH: 0957.62034
MathSciNet: MR2001B:62082
Digital Object Identifier: 10.1214/aos/1017939150

Subjects:
Primary: 62G05, 62G30, 62H12, 62J05

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 5 • October 1999
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