- Volume 19, Number 5B (2013), 2200-2221.
Dominance properties of constrained Bayes and empirical Bayes estimators
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.
Bernoulli, Volume 19, Number 5B (2013), 2200-2221.
First available in Project Euclid: 3 December 2013
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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
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