Abstract

Likelihood ration, confidence bands in non-parametric regression with censored data

LI G. and I. VAN KEILEGOM

Let (X,Y) be a random vector, where Y denotes the variable of interest possibly subject to random right censoring, and X is a covariate. We construct confidence intervals and bands for the conditional survival and quantile function of Y given X using a non-parametric likelihood ratio approach. This approach was introduced ty Thomas & Grunkemeier (1975), who estimated confidence intervals of survival probabilities based on right censored data. The methods is appealing for several reasons: it always produces intervals inside [0,1], it does not involve variance estimation, and can produce aymmetric intervals. Asymptotic results for the confidence intervals and bands are obtained, as well as simulation results in which the performance of the likelihood ratio intervals and bands is compared with that of the normal approximation method. We also propose a bandwidth selection procedure based on the bootstrap and apply the technique on a real data set.

  Last update: January, 24, 2003  - Contact : S. Malali