Sampling Weight Calibration with Estimated Control Totals

Abstract

Sample weight calibration, also referred to as calibration estimation, is a widely applied technique in the analysis of survey data. This method borrows strength from a set of auxiliary variables and can produce weighted estimates with smaller mean square errors than those estimators that do not use the calibration adjustments. Poststratification is a well-known calibration method that forces weighted counts within cells generated by cross-classifying the categorical (or categorized) auxiliary variables to equal the corresponding population control totals.

Several assumptions are critical to the theory developed to date for weight calibration. Two assumptions relevant to this research include: (i) the control totals calculated from the population of interest and known without (sampling) error; and (ii) the sample units selected for the survey are taken from a sampling frame that completely covers the population of interest (e.g., no problems with frame undercoverage).

With a few exceptions, research to date generally is conducted as if these assumptions hold, or that any violation does not affect estimation. Our research directly examines the violation of the two assumptions by evaluating the theoretical and empirical properties of the mean square error for a set of calibration estimators, newly labeled as estimated-control (EC) calibration estimators. Specifically, this dissertation addresses the use of control totals estimated from a relatively small survey to calibrate sample weights for an independent survey suffering from undercoverage and sampling errors. The EC calibration estimators under review in the current work include estimated totals and ratios of two totals, both across all and within certain domains. The ultimate goal of this research is to provide survey statisticians with a sample variance estimator that accounts for the violated assumptions, and has good theoretical and empirical properties.