ON ESTIMATING DISTRIBUTION-FUNCTIONS USING NOMINATION SAMPLES

A nomination sample consists of independently distributed maxima from subsamples of a population with the same underlying distribution. Nomi nation sampling occurs when only the item with largest value is chosen from each of n independent subsamples. If the subsamples differ in si ze, then these observed order statistics are not identically distribut ed, so estimation schemes built on assumptions of independently and id entically distributed (iid) data are most likely inappropriate. But we can exploit the structure of the data from the nomination sample by c onditioning 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 o ne found in Ferguson, where the case for iid data is presented. The re sult 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 Kolmo gorov-Smirnov distance.