Looking for optimal auxiliary variables in sample survey quantile estimation

Abstract

We address the problem of selecting between two (available) auxiliary variables for computing optimal quantile estimators in finite population survey sampling. The assumed asymptotic perspective allow us to derive optimal conditions for auxiliary variables when a wide class of estimators is considered, under an arbitrary sampling design. For a simple random sampling design we particularize the asymptotic results and it yields simple and meaningful conditions which can be evaluated in practise in a fast and easy way. An empirical study involving several natural finite populations and small sample sizes confirms the asymptotics.