Large sample theory of a modified Buckley-James estimator for regression analysis with censored data. (English) Zbl 0742.62043

Lai, Tze Leung; Ying, Zhiliang

Ann. Stat. 19, No. 3, 1370-1402 (1991).

Summary: J. Buckley and I. James [Biometrika 66, 429-436 (1979; Zbl 0425.62051)] proposed an extension of the classical least squares estimator to the censored regression model. It has been found in some empirical and Monte Carlo studies that their approach provides satisfactory results and seems to be superior to other extensions of the least squares estimator in the literature. To develop a complete asymptotic theory for this approach, we introduce herein a slight modification of the Buckley-James estimator to get around the difficulties caused by the instability at the upper tail of the associated Kaplan-Meier estimate of the underlying error distribution and show that the modified Buckley-James estimator is consistent and asymptotically normal under certain regularity conditions.
A simple formula for the asymptotic variance of the modified Buckley- James estimator is also derived and is used to study the asymptotic efficiency of the estimator. Extensions of these results to the multiple regression model are also given.

MSC:

62G07	Density estimation
62G20	Asymptotic properties of nonparametric inference
62J05	Linear regression; mixed models

Keywords:

stochastic integral representations; nonparametric regression; empirical process; martingale; least squares estimator; censored regression model; Kaplan-Meier estimate; modified Buckley-James estimator; consistent; asymptotically normal; asymptotic variance; asymptotic efficiency; multiple regression model

Citations:

Zbl 0425.62051