On Estimating Distribution Functions Using Nomination Samples
研究了当从不同大小的子样本中仅选取最大值（提名样本）时，如何利用这些非独立同分布数据构造分布函数的最小二乘估计量，该估计量一致且均方误差优于非参数最大似然估计。
Abstract A nomination sample consists of independently distributed maxima from subsamples of a population with the same underlying distribution. Nomination sampling occurs when only the item with largest value is chosen from each of n independent subsamples. If the subsamples differ in size, then these observed order statistics are not identically distributed, so estimation schemes built on assumptions of independently and identically distributed (iid) data are most likely inappropriate. But we can exploit the structure of the data from the nomination sample by conditioning on the observed order of the independent maxima, and form a least squares estimator of the distribution function that minimizes risk with respect to squared error loss using an approach similar to one found in Ferguson, where the case for iid data is presented. The result is a product estimator that is consistent and compares favorably with the nonparametric maximum likelihood estimator proposed by Boyles and Samaniego, as indicated by graphs of mean squared error and Kolmogorov-Smirnov distance. Key Words: Conditional riskKolmogorov-Smirnov statisticLeast squares estimation