F. Liese, I. Steinke
A simplified approach to the Hajek-LeCam bound
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
62F05 Asymptotic properties of tests
62F12 Asymptotic properties of estimators
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 Hajek-LeCam bound which represents a lower bound for the
maximum risk of a sequence of decisions.
It is given a simplified proof for the existence of accumulation points
of a sequence of generalized decisions functions using the
$\varepsilon$-Blackwell sufficiency of sufficient statistics defined
on finite experiments. That is the main step for deriving the Hajek-LeCam
bound for weakly convergent sequences of experiments.
Keywords: Hajek-LeCam bound, weakly convergent experiments, generalized decision function