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May, 1977 Improved Rates in the Empirical Bayes Monotone Multiple Decision Problem $\operatorname{MLR}$ Family
Dennis C. Gilliland, James Hannan
Ann. Statist. 5(3): 516-521 (May, 1977). DOI: 10.1214/aos/1176343848


In the context of the two-action, linear loss, exponential family multiple decision problem, Van Houwelingen (1973), (1976) has shown that faster rates of convergence are deducible for monotone empirical Bayes procedures than result from application of the bound established for general empirical Bayes procedures by Johns and Van Ryzin (1972). This note generalizes a (1973) Van Houwelingen bound to arbitrary $k$-action, monotone loss, MLR family multiple decision problems. An example is given to show that the result is a useful alternative to the recent Van Ryzin and Susarla (1977) multiple decision problem generalization of Johns and Van Ryzin.


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Dennis C. Gilliland. James Hannan. "Improved Rates in the Empirical Bayes Monotone Multiple Decision Problem $\operatorname{MLR}$ Family." Ann. Statist. 5 (3) 516 - 521, May, 1977.


Published: May, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0358.62007
MathSciNet: MR440753
Digital Object Identifier: 10.1214/aos/1176343848

Primary: 62C25
Secondary: 62F99

Keywords: Empirical Bayes , monotone likelihood ratio family , monotone multiple decision problem

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 3 • May, 1977
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