Confidence Bands for a Survival Curve from Censored Data
针对右删失数据，基于Kaplan-Meier估计量构建生存函数的大样本同时置信带，通过变换使极限过程成为布朗桥，并给出无删失时退化为Kolmogorov带的性质。
For arbitrarily right-censored data, the Kaplan-Meier product-limit estimator Ŝ 0N provides a nonparametric estimate of the survival function S 0 = 1 − F 0 . We provide large-sample simultaneous confidence bands for S 0 , centred at Ŝ 0N . The derivation uses the weak convergence of N½ { Ŝ 0N ( t ) − S 0 ( t )}, on a finite interval, to a Gaussian process, a theorem of Breslow & Crowley (1974), and transforms both the time and space axes of the limiting process to achieve a Brownian bridge limit. Parameters in the transformation are replaced by uniformly consistent estimates to form the bands. The new bands reduce to the well-known Kolmogorov bands in the absence of censoring. Comparisons are made with recent bands of Gillespie & Fisher (1979) and V. N. Nair. The bands are illustrated by imposing some different kinds of random censorship on a set of uncensored data.