On calibration of design weights

TL;DR

This paper explores the relationship between different estimators in survey sampling, emphasizing the importance of calibration of weights and proposing modifications for statistical software to improve accuracy.

Contribution

It establishes a theoretical connection between the GREG and linear regression estimators and suggests modifications for statistical packages to enhance calibration procedures.

Findings

Confirmed the sum of calibrated weights should equal the sum of design weights.

Provided a theoretical bridge between GREG and linear regression estimators.

Suggested modifications for statistical software like GES and SUDAAN.

Abstract

In the present investigation, we build a bridge between the generalized regression (GREG) estimator due to Deville and Sarndal (1992) and the linear regression estimator due to Hansen, Hurwitz and Madow (1953) in the presence of single auxiliary variable. The bridge confirms that the sum of calibrated weights should be equal to sum of design weights as pointed out by Singh (2003, 2004, 2006) and Stearns and Singh (2008). An important modification in the statistical packages such as GES, SUDAAN etc. has been suggested.