Estimation of a finite population distribution function based on a linear model with unknown heteroscedastic errors

The authors consider a finite population P = {(Y-k, x(k)), k = 1,..., N} conforming to a linear superpopulation model with unknown heteroscedastic errors, the variances of which are values of a smooth enough function of the auxifiary variable X for their nonparametric estimation. They describe a method of the Chambers-Dunstan type for estimation of the distribution of { Y-k, k = 1,..., N} from a sample drawn from P without replacement, and determine the asymptotic distribution of its estimation error. They also consider estimation of its mean squared error in particular cases, evaluating both the analytical estimator derived by "plugging-in" the asymptotic variance, and a bootstrap approach that is also applicable to estimation of parameters other than mean squared error. These proposed methods are compared with some common competitors in simulation studies.