Building Block Small Area Model for Compatibility at Different Levels of Estimation

• Activity Number: 567 - Recent Advances in Small Area Estimation with Applications and Evaluation of the Estimates
• Type: Topic Contributed
• Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Government Statistics Section
• Author(s): Adrijo Chakraborty* and Avinash Singh
• Companies: NORC at the University of Chicago and American Institutes for Research
• Keywords: Small area estimation ; Building block model ; Hierarchical Bayes

Abstract

Higher (H) level models for small area estimation (SAE) of totals can be derived from the building block (BB) model of Singh (2006); BB denotes the lowest area with available auxiliary data. Traditionally, separate Fay-Herriot models at H-levels containing BBs are defined but they become incompatible with regard to exchangeability assumptions of random effects when the underlying BB model is true. In practice, direct estimates for several BBs may not be available and groups (G) of BBs are formed to obtain useful direct estimates with a somewhat stable estimated V-C matrix. The G-level model is used to estimate fixed parameters in the mean function and variance components but separate sets of estimates for all B-level random effects are obtained from modeling each H-level of interest for design consistency of resulting SAEs. Despite the unavailability of direct estimates for several BBs, the proposed approach produces nonsynthetic SAEs for all such BBs. Both Bayesian and frequentist methods for SAE are considered under alternative strategies for grouping. Benefits of the proposed approach are explained and illustrated through a simulation study.