Standard Regression Model-Based Small-Area Domain Estimation in Household Surveys

• Activity Number: 37
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Prabhakar Ghangurde*+
• Keywords: model-based ; domain ; estimation ; BLUP ; BLUE ; Type-B

Abstract

Assuming known auxiliary variable domain means model-based estimator of domain mean of estimation variable is derived as regression-synthetic estimator. In the case of one auxiliary variable weighted least squares estimator of domain mean of estimation variable is ratio-synthetic estimator,which is design-consistent and BLUE; it is extended to post-strata. Assuming known x-total and y-values of units in complementary domain to be zero, model-based estimator of domain y-total is design-consistent and BLUE. It is extended to post-strata and reduced to synthetic estimator with ratio-adjustment, by making well-known assumption of synthetic estimation within each post-stratum, and then to ratio-synthetic estimator by a simple substitution. Under the model the assumption in ratio-synthetic estimation is the same as in synthetic estimation; it is referred to as borrowing strength for the domain from the population. The model is extended as a mixed model to derive BLUP estimator as extension of ratio-synthetic estimator assuming sampling of clusters of households and unequal error variances. The model with equal variances for units is obtained as a particular case of the mixed model.