A New Perspective on Calibration Estimators

• Activity Number: 455
• Type: Invited
• Date/Time: Thursday, August 7, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Victor Estevao*+ and Carl E. Sarndal
• Companies: Statistics Canada and Universite de Montreal
• Keywords: automated linearization ; instrument vector ; auxiliary information ; approximate variance ; design-based approach

Abstract

Calibration is a widely used method of estimation in sample surveys, but there are differing views on the derivation of these estimators. We use a design-based approach with a new perspective on the use of auxiliary information. We start with a general form for the calibration weights, parameterized by an instrument vector z. We outline an "automated linearization" technique to easily obtain the approximate (asymptotic) variance of the calibration estimator. This allows us to find an optimal z, in the sense of minimizing the approximate variance. This perspective is in contrast with the modeling approach, which is based on the idea of model fitting. We first describe this technique in single-phase sampling. The auxiliary information is then relatively simple, consisting of sample auxiliary variables and their known population totals. The auxiliary information is usually more complex in two-stage or two-phase sampling. For these designs, we consider different ways to link the weights of units at different levels of sampling. We show how to use our automated linearization technique to easily obtain the approximate variance of the resulting calibration estimators.