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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

journal of applied mathematics and stochastic analysis

Convergence rates for empirical Bayes two-action problems: the uniform <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$U\left( {0,\theta } \right)$ "><mml:mrow><mml:mi>U</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>θ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> distribution

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