A Kernel-Type Estimator of a Quantile Function From Right-Censored Data
针对右删失寿命数据，提出一种比传统乘积限估计更平滑的分位数函数核型估计量，证明其强相合性，并通过模拟和机械开关寿命数据验证其均方误差更小。
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.