JSM 2004 - Toronto

Abstract #300047

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Activity Number: 420
Type: Invited
Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #300047
Title: Weighted Empirical Likelihood
Author(s): Jian-Jian Ren*+
Companies: University of Central Florida
Address: Department of Mathematics, Orlando, FL, 32816,
Keywords: empirical likelihood ; bootstrap ; right-censored data ; doubly censored data ; interval-censored data ; quantiles
Abstract:

Weighted empirical likelihood is a newly developed likelihood method which can be used to construct tests and confidence intervals for various types of incomplete data, such as right-censored data, doubly censored data, interval-censored data and partly interval-censored data.So far, there has not been any published work on likelihood-based interval estimate for quantiles with doubly censored data, partly interval-censored data, or interval-censored data. We give a rather general theorem for constructing Weighted Empirical Likelihood Ratio Confidence Intervals (WELRCI) which include the mean, survival probabilities, median, quantiles, M-statistic, and trimmed mean as special cases. Also, a general theoretical coverage accuracy equation for WELRCI is established under a unified framework for various types of censored data. In particular, it is shown that the coverage accuracy of WELRCI for survival probabilities and quantiles with right-censored data is at least O(n^{-1/2}). Theory and simulation show that WELRCI is accurate and efficient, and the use of the n out n bootstrap in its implementation appears to give satisfactory performance in all cases considered.

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