Variance reduction through location shifts in unequal probability sampling (Q1116217)

Sometimes a change of origin of a quantitative survey variable is sufficient to reduce the variance of the Horvitz-Thompson estimator of the total in unequal probability sampling. \textit{A. Stuart} [J. R. Stat. Soc., Ser. A 149, 349-365 (1986; Zbl 0608.62009)] calls this operation ``location-shift''. In the present paper this technique is studied, in a more general framework, with regard to an assumed superpopulation model, and some results are extended to stratified sampling designs. Furthermore, theoretical and empirical evidence is given of the advantages of this technique under certain conditions.