Estimation of the finite population distribution function using a global penalized calibration method

摘要

Auxiliary information x is commonly used in survey sampling at the estimation stage. We propose an estimator of the finite population distribution function Fy( t) when x is available for all units in the population and related to the study variable y by a superpopulation model. The new estimator integrates ideas from model calibration and penalized calibration. Calibration estimates of Fy( t) with the weights satisfying benchmark constraints on the fitted values distribution function ^ F ^ y = F ^ y on a set of fixed values of t can be found in the literature. Alternatively, our proposal ^ F y. seeks an estimator taking into account a global distance D( ^ F ^ y., F ^ y) between ^ F ^ y. and F ^ y, and a penalty parameter a that assesses the importance of this term in the objective function. The weights are explicitly obtained for the L2 distance and conditions are given so that ^ F y. to be a distribution function. In this case ^ F y. can also be used to estimate the population quantiles. Moreover, results on the asymptotic unbiasedness and the asymptotic variance of ^ F y., for a fixed a, are obtained. The results of a simulation study, designed to compare the proposed estimator to other existing ones, reveal that its performance is quite competitive.