Estimation of domain means on the basis of strategy dependent on depth function of auxiliary variables' distribution

Abstract

The paper deals with the problem of estimation of a domain means in a finite and fixed population. We assume that observations of a multidimensional auxiliary variable are known in the population. The proposed estimation strategy consists of the well known Horvitz-Thompson estimator and the non-simple sampling design dependent on a synthetic auxiliary variable whose observations are equal to the values of a depth function of the auxiliary variable distribution. The well known spherical and Mahalanobis depth functions are considered. A sampling design is proportionate to the maximal order statistic determined on the basis of the synthetic auxiliary variable observations in a simple sample drawn without replacement. A computer simulation analysis leads to the conclusion that the proposed estimation strategy is more accurate for domain means than the well known simple sample means