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 H\'{a}jek--LeCam bound which is an asymptotic lower bound for the maximum risk of a sequence of decisions. To give a simplified proof for the H\'{a}jek-LeCam bound we use the concept of approximate Blackwell--sufficiency.