Dominance properties of constrained Bayes and empirical Bayes estimators

Tatsuya Kubokawa, William E. Strawderman

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

This paper studies decision theoretic properties of benchmarked estimators which are of some importance in small area estimation problems. Benchmarking is intended to improve certain aggregate properties (such as study-wide averages) when model based estimates have been applied to individual small areas. We study decision-theoretic properties of such estimators by reducing the problem to one of studying these problems in a related derived problem. For certain such problems, we show that unconstrained solutions in the original (unbenchmarked) problem give unconstrained Bayes and improved estimators which automatically satisfy the benchmark constraint. Also, dominance properties of constrained empirical Bayes estimators are shown in the Fay-Herriot model, a frequently used model in small area estimation.

Original languageEnglish (US)
Pages (from-to)2200-2221
Number of pages22
JournalBernoulli
Volume19
Issue number5 B
DOIs
StatePublished - Nov 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Keywords

  • Admissibility
  • Benchmark
  • Constrained Bayes estimator
  • Decision theory
  • Dominance result
  • Empirical Bayes
  • Fay-Herriot model
  • Minimaxity
  • Multivariate normal distribution
  • Quadratic loss function
  • Risk function
  • Small area estimation

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