Quantile estimation based on nomination sampling

Nomination sampling is a sampling process in which every observation is the maximum of a random sample from some distribution. If all samples are taken from a single underlying CDF, F, data can be viewed as consisting of pairs (X/sub i/,K/sub i/) where K/sub i/ is the size of sample i and, given K/sub i/=k/sub i/, X/sub i/ is distributed according to CDF F/sup ki/. R.A. Boyles and F.J. Samaniego (1986) developed a nonparametric maximum-likelihood estimator of F. In the present work, their approach is extended to obtain estimates of the quantiles of F and to study the limit theory and consistency properties of these estimates. These results generalize the results of T.R. Willemain (1980), who discussed the estimation of the median of F based on nomination samples.<>