Re-calibration of sample means

TL;DR

This paper examines the calibration problem and the GREG estimator, revealing its limitations in variance minimization, and proposes a new estimator that is unbiased and asymptotically achieves minimal variance.

Contribution

It introduces a new estimator that improves upon the GREG method by being unbiased and asymptotically minimizing variance.

Findings

GREG estimator is not asymptotically minimal variance unbiased.

Proposed estimator is unbiased and asymptotically has minimal variance.

Abstract

We consider the problem of calibration and the GREG method as suggested and studied in Deville and Sarndal (1992). We show that a GREG type estimator is typically not minimal variance unbiased estimator even asymptotically. We suggest a similar estimator which is unbiased but is asymptotically with a minimal variance.