EMPIRICAL LIKELIHOOD FOR A CLASS OF FUNCTIONALS OF SURVIVAL DISTRIBUTION WITH CENSORED DATA

QI-HUA WANG AND BING-YI JING

1Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Science, Beijing, 10080, China

2Department of Mathematics, Hong Kong University of Science and Technology, Kowloon, Hong Kong, e-mail: majing@ust.hk

(Received May 24, 1999; revised March 6, 2000)

Abstract. The empirical likelihood was introduced by Owen, although its idea originated from survival analysis in the context of estimating the survival probabilities given by Thomas and Grunkemeier. In this paper, we investigate how to apply the empirical likelihood method to a class of functionals of survival function in the presence of censoring. We define an adjusted empirical likelihood and show that it follows a chi-square distribution. Some simulation studies are presented to compare the empirical likelihood method with the Studentized-t method. These results indicate that the empirical likelihood method works better than or equally to the Studentized-t method, depending on the situations.

Key words and phrases: Empirical likelihood, censoring, Kaplan-Meier estimate, survival probability, mean lifetime, Studentized-t.