Bernoulli

  • Bernoulli
  • Volume 19, Number 5B (2013), 2200-2221.

Dominance properties of constrained Bayes and empirical Bayes estimators

Tatsuya Kubokawa and William E. Strawderman

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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.

Article information

Source
Bernoulli, Volume 19, Number 5B (2013), 2200-2221.

Dates
First available in Project Euclid: 3 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1386078600

Digital Object Identifier
doi:10.3150/12-BEJ449

Mathematical Reviews number (MathSciNet)
MR3160551

Zentralblatt MATH identifier
1281.62037

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

Citation

Kubokawa, Tatsuya; Strawderman, William E. Dominance properties of constrained Bayes and empirical Bayes estimators. Bernoulli 19 (2013), no. 5B, 2200--2221. doi:10.3150/12-BEJ449. https://projecteuclid.org/euclid.bj/1386078600


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