WEIGHTED EMPIRICAL LIKELIHOOD RATIO CONFIDENCE INTERVALS FOR THE MEAN WITH CENSORED DATA

JIAN-JIAN REN

Department of Mathematics, Tulane University, New Orleans, LA70118, U.S.A.

(Received June 25, 1998; revised June 7, 1999)

Abstract. We propose a procedure to construct the empirical likelihood ratio confidence interval for the mean using a resampling method. This approach leads to the definition of a likelihood function for censored data, called weighted empirical likelihood function. With the second order expansion of the log likelihood ratio, a weighted empirical likelihood ratio confidence interval for the mean is proposed and shown by simulation studies to have comparable coverage accuracy to alternative methods, including the nonparametric bootstrap-t. The procedures proposed here apply in a unified way to different types of censored data, such as right censored data, doubly censored data and interval censored data, and computationally more efficient than the bootstrap-t method. An example of a set of doubly censored breast cancer data is presented with the application of our methods.

Key words and phrases: Bootstrap, doubly censored data, interval censored data, leveraged bootstrap, right censored data.