Abstract: The empirical Bayes test problem of parameter for a class of continuous one-parameter exponential family is considered in this paper. By using the recursive kernel esti-mation of probability density function and monotonicity of Bayes test function in the case of independent and identically distributed samples, the EB test function in established for a class of continuous one-parameter exponential family. By the construction method of modifying EB test function, the monotone Bayes test function are constructed. In addition, convergence rates of EB test function are obtained under the suitable conditions, and the results of convergence rate order are improved. Finally, a numerical example is presented to verify the conditions of the theorem.

Key words: the kernel estimation of density function, monotone Bayes test, the empirical Bayes test, convergence rates