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Information Theory and Superefficiency

Andrew Barron and Nicolas Hengartner
The Annals of Statistics
Vol. 26, No. 5 (Oct., 1998), pp. 1800-1825
Stable URL: http://www.jstor.org/stable/120022
Page Count: 26
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Information Theory and Superefficiency
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Abstract

The asymptotic risk of efficient estimators with Kullback-Leibler loss in smoothly parametrized statistical models is k/2n, where k is the parameter dimension and n is the sample size. Under fairly general conditions, we given a simple information-theoretic proof that the set of parameter values where any arbitrary estimator is superefficient is negligible. The proof is based on a result of Rissanen that codes have asymptotic redundancy not smaller than (k/2)log n, except in a set of measure 0.

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