Stability of relaxed calibration

TL;DR

This paper investigates the stability of calibration estimators when additional auxiliary variables are included, providing an upper bound on estimate changes to assess the value of further data sources.

Contribution

It introduces a method to quantify the sensitivity of calibration estimates to auxiliary variable inclusion, aiding decisions on data collection.

Findings

Provides an upper bound for estimate change with added variables

Offers a measure of estimate sensitivity to auxiliary information

Helps determine the necessity of additional data sources

Abstract

Estimation of the population total of a variable can be improved by calibration on a set of auxiliary variables. It is difficult to establish that such a set of variables is sufficient, that estimation could not be improved by calibration on any further variables. We address this issue by finding an upper bound for the change of the calibration estimate of the population total of a variable when the auxiliary information is supplemented by another variable for which the population total is known. This upper bound can be interpreted as a measure of sensitivity of the estimate to unavailable auxiliary information and considered as a factor in deciding whether to seek further data sources that would be included in calibration.