Estimation of the quantile function of residual life time distribution

Abstract

The estimation of the quantile function of the residual life time distribution is of interest in life testing. Since the sample quantile function (empirical estimator) of the residual life is discontinuous, we smooth the function by convolving it with a kernel function. The smoothed function is called a kernel-type estimator. We study the asymptotic properties of the kernel-type estimator and the empirical estimator. Specifically, we consider the convergence in mean squared error. Empirical results are given on the small sample properties of the two estimators, based on a Monte Carlo simulation study.