Convergence rates for empirical Bayes two-action problems: the uniform U(0, θ) distribution. (1992)

• Record Type: Journal Article
• Authors: Tahir, Mohamed
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 5:Number 2(1992)
• Page Start: 167
• Page End: 175
• Publication Date: 1992
• Subjects: asymptotically optimal -- Bayes risk -- convergence rates -- empirical Bayes decision rule -- prior distribution; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953392000145
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : The purpose of this paper is to study the convergence rates of a sequence of empirical Bayes decision rules for the two-action problems in which the observations are uniformly distributed over the interval ( 0, θ ), where θ is a value of a random variable having an unknown prior distribution. It is shown that the proposed empirical Bayes decision rules are asymptotically optimal and that the order of associated convergence rates is O ( n − α ), for some constant α, 0 < α < 1, where n is the number of accumulated past observations at hand.