A BOOTSTRAP APPROACH TO NONPARAMETRIC REGRESSION FOR RIGHT CENSORED DATA

GANG LI^{1}, AND SOMNATH DATTA^{2}

1Department of Biostatistics, School of Public Health, University of California, Los Angeles,

CA 90095-1772, U.S.A.

2Department of Statistics, Franklin College of Arts and Sciences, University of Georgia, 204 Statistics Building, Athens, GA 30602-1952, U.S.A., e-mail: datta@stat.uga.edu

(Received May 13, 1999; revised April 4, 2000)

Abstract. In this paper a two-stage bootstrap method is proposed for nonparametric regression with right censored data. The method is applied to construct confidence intervals and bands for a conditional survival function. Its asymptotic validity is established using counting process techniques and martingale central limit theory. The performance of the bootstrap method is investigated in a Monte Carlo study. An illustration is given using a real data.

Key words and phrases: Bootstrap, Beran’s estimate, censoring, confidence bands, confidence intervals, Kaplan-Meier estimate, nonparametric regression, quantile regression.