Empirical estimates with minimal $d$-risk for discrete exponential families

We develop a $d$-posteriori approach to estimations with uniformly minimal $d$-risk, when the a priori distribution is completely unknown. For a scalar parameter of a discrete exponential family we construct empirical estimates based on archive data and prove the convergence of the empirical $d$-risk to the true one. As an example we adduce the estimation of the Poisson distribution parameter. We numerically study the accuracy of the estimates by the statistical modeling method.