Empirical Bayes two-action problem for the continuous one-parameter exponential family with errors in variables

In this paper we study the empirical Bayes linear-loss two-action problem for the continuous one-parameter exponential family when the observed data are contaminated (errors in variables). A new empirical Bayes testing rule is constructed, and its asymptotic optimality uniformly over a class of prior distributions is established. Uniform rates of convergence of the corresponding regret (excess risk), which depends on the type of the error distribution, are also obtained for two types of error distributions. Our results are compared with the `pureʹ observed data results of the literature.