## The Annals of Statistics

### Information theory and superefficiency

#### Abstract

The asymptotic risk of efficient estimators with Kullback–Leibler loss in smoothly parametrized statistical models is $k/2_n$, 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.

#### Article information

Source
Ann. Statist., Volume 26, Number 5 (1998), 1800-1825.

Dates
First available in Project Euclid: 21 June 2002

https://projecteuclid.org/euclid.aos/1024691358

Digital Object Identifier
doi:10.1214/aos/1024691358

Mathematical Reviews number (MathSciNet)
MR1673279

Zentralblatt MATH identifier
0932.62005

Subjects
Primary: 62F12 94A65
Secondary: 94A29 62G20

#### Citation

Barron, Andrew; Hengartner, Nicolas. Information theory and superefficiency. Ann. Statist. 26 (1998), no. 5, 1800--1825. doi:10.1214/aos/1024691358. https://projecteuclid.org/euclid.aos/1024691358

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• NEW HAVEN, CONNECTICUT 06520-8290 E-MAIL: barron@stat.yale.edu nicolas.hengartner@yale.edu