On moments of generalized Bayessian estimators and maximum likelihood estimators

The main results of this paper are the Theorems 1 and 2 and in particular, inequali ties (3.2). These theorems consider properties of the Bayessian estimates $\widetilde\theta_n$ for a wide class of a priory densities and cost functions. Precise conditions are formulated in Section 2 (see conditions A$_1$–A$_3$, Б$_1$–Б$_5$). Analogous theorems are proved in Section 7 for the maximum likelihood estimate under some additional conditions.