  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.
