Empirical Likelihood for Right Censored Lifetime Data

When the empirical likelihood (EL) of a parameter θ is constructed with right censored data, literature shows that − 2log (empirical likelihood ratio) typically has an asymptotic scaled chi-squared distribution, where the scale parameter is a function of some unknown asymptotic variances. Therefore, the EL construction of confidence intervals for θ requires an additional estimation of the scale parameter. Additional estimation would reduce the coverage accuracy for θ. By using a special influence function as an estimating function, we prove that under very general conditions, − 2log (empirical likelihood ratio) has an asymptotic standard chi-squared distribution with one degree of freedom. This eliminates the need for estimating the scale parameter as well as eases some of the often demanding computations of the EL method. Our estimating function yields a smaller asymptotic variance than those of Wang and Jing (2001) and Qin and Zhao (2007). Thus, it is not surprising that confidence intervals using the special influence functions give a better coverage accuracy as demonstrated by simulations.