Some improved estimators of finite population quantile using auxiliary information in sample surveys

Abstract

The problem of quantile estimation using quantiles Q x ( α) in which the order of the auxiliary variable is different from that of the main variable to be estimated, Q y ( β), is considered. Certain new estimators for the β-quantile have been proposed for any sampling design. The effect of this modification on the standard estimators, ratio, position, stratification, regression and difference type estimators which use the β-quantile of the auxiliary variable to estimate the β-quantile of the main variable, is studied. On the basis of properties derived and some simulation results, the efficiencies of these estimators are compared. It is shown that by the appropriate choice of the α order of the quantile, it is possible to obtain a considerable increase in precision with respect to standard estimators. In simple random sampling, a procedure for choosing the α value is proposed.