Empirical likelihood for right censored data with covariables

Abstract

For complete observation and p-dimensional parameter θ defined by an estimation equation, empirical likelihood method of construction of confidence region is based on the asymptotic χ ² _p distribution of −2 log(EL ratio). For right censored lifetime data with covariables, however, it is shown in literature that −2 log(EL ratio) converges weakly to a scaled χ ² _p distribution, where the scale parameter is a function of unknown asymptotic covariance matrix. The construction of confidence region requires estimation of this scale parameter. In this paper, by using influence functions in the estimating equation, we show that −2 log(EL ratio) converges weakly to a standard χ ² _p distribution and hence eliminates the procedure of estimating the scale parameter.