Abstract:

Let $E_n$ be a sequence of experiments weakly converging to a limit experiment $E$. One of the basic objectives of asymptotic decision theory is to derive asymptotically "best" decisions in $E_n$ from optimal decisions in the limit experiment $E$. A central statement in this context is the Hájek-LeCam bound which is an asymptotic lower bound for the maximum risk of a sequence of decisions. To give a simplified proof for the Hájek-LeCam bound we use the concept of approximate Blackwell-sufficiency.