A Kernel-Type Estimator of a Quantile Function from Right-Censored Data

Abstract Based on right-censored data from a lifetime distribution F 0, a kernel-type estimator of the quantile function Qo (p) = inf{t: F 0(t) ≧ p}, 0 ≦ p ≦ 1, is proposed. The estimator is defined by , which is smoother than the usual product-limit quantile function , where denotes the product-limit estimator of F 0 from the censored sample. Under the random censorship model and general conditions on hn, K, and F 0, it is shown that Qn (p) is strongly consistent. In addition, an approximation to Qn is shown to be asymptotically equivalent to Qn with probability one. A small Monte Carlo simulation study shows that for several values of the bandwidth hn, Qn performs better than in the sense of estimated mean squared errors. An optimal bandwidth hn may be estimated by bootstrap methods in some cases. The procedure is illustrated by an application to data from a mechanical-switch life test.