Properties of the Combined Ratio Estimator and a Best Linear Unbiased Estimator When Design Control Is Problematic

• Activity Number: 427
• Type: Contributed
• Date/Time: Wednesday, August 1, 2007 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Stephen Woodruff*+
• Companies: Retired
• Keywords: Combined Ratio Estimator ; Self-Weighting Design ; Best Linear Unbiased Estimation ; Stratified Cluster Designs

Abstract

This is a study of a Best Linear Unbiased Estimator (BLUE) and the Combined Ratio Horwitz-Thompson Estimator (CRHT) for sampling problems where efficient self-weighting designs are impractical. Sampling of mail is an example of this. A measure for "self-weighting" is derived and their variances as functions of this measure are compared under repeated sampling from stratified cluster designs. For self-weighting designs, the variances of CRHT and BLUE are similar but that of CRHT increases rapidly as the measure increases. The BLUE is insensitive to the measure. When design control is impossible, the variance of CRHT can be many times (2 to 100s) that of the BLUE. The BLUE is derived from mail population characteristics and the sample design, making model failure a virtual non-issue. Simulation results, supporting mathematics, their implications, and applications are presented.