Jackknife Empirical Likelihood Inference for the Variance Residual Life Function

Abstract

In life testing situations, the residual life time of a component which has survived t units of time is X_t = X −t|X > t. In this paper, we give a central limit theorem result for the estimator of Var(X_t), the variance residual life(VRL) function. The result is used to construct normal approximation based confidence interval for the VRL. Furthermore, we use the jackknife empirical likelihood ratio procedure to obtain confidence interval for the VRL function. These intervals are compared through simulation study in terms of the average length and coverage probability. Finally, a numerical example illustrating the theory is also given.