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_i,K_i) where K_i is the size of sample i and, given K_i=k_i, X_i is distributed according to CDF F^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