Lower bounds of minimax risk in estimation problems without lan condition

Abstract

We consider the problems of minimax estimation in an asymptotic setting for quite general statistical models. In particular, we do not require that the well-known LAN condition holds. We show that general statistical experiments which correspond to a random number of dependent observations can be approximated by experiments of a special form called -models. Then we obtain lower bounds for minimax estimation risk for -models. This allows us to obtain lower bounds for asymptotic minimax risk for a wide class of statistical models