Empirical Bayes Test for the Parameter of Rayleigh Distribution with Error of Measurement

Abstract

For the data with error of measurement in historical samples, the empirical Bayes test rule for the parameter of Rayleigh distribution is constructed, and the asymptotically optimal property is obtained. It is shown that the convergence rate of the proposed EB test rule can be arbitrarily close to $O(n^{−\frac{1}{2}})$ under suitable conditions.