A note on the Hájek-LeCam bound. (English) Zbl 0934.62010

Summary: 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.


62B15 Theory of statistical experiments
62B05 Sufficient statistics and fields
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