Empirical Likelihood for Right Censored Lifetime Data

TL;DR

This paper develops an improved empirical likelihood method for constructing confidence intervals for linear functionals in right censored lifetime data, eliminating the need to estimate scale parameters and improving coverage accuracy.

Contribution

It introduces a novel influence function approach that ensures log EL converges to a standard chi-square distribution without estimating scale parameters, simplifying computations and enhancing accuracy.

Findings

Eliminates the need for scale parameter estimation in EL for censored data.

Achieves smaller asymptotic variance of influence functions compared to previous methods.

Demonstrates improved coverage accuracy through simulations.

Abstract

This paper considers the empirical likelihood (EL) construction of confidence intervals for a linear functional based on right censored lifetime data. Many of the results in literature show that log EL has a limiting scaled chi-square distribution, where the scale parameter is a function of the unknown asymptotic variance. The scale parameter has to be estimated for the construction. Additional estimation would reduce the coverage accuracy for the parameter. This diminishes a main advantage of the EL method for censored data. By utilizing certain influence functions in an estimating equation, it is shown that under very general conditions, log EL converges weakly to a standard chi-square distribution and thereby eliminates the need for estimating the scale parameter. Moreover, a special way of employing influence functions eases the otherwise very demanding computations of the EL method. Our approach yields smaller asymptotic variance of the influence function than those comparable ones considered by Wang and Jing (2001) and Qin and Zhao (2007). Thus it is not surprising that confidence intervals using influence functions give a better coverage accuracy as demonstrated by simulations.