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December, 1989 On the Asymptotic Information Bound
Aad van der Vaart
Ann. Statist. 17(4): 1487-1500 (December, 1989). DOI: 10.1214/aos/1176347377


This paper discusses several lower bound results for the asymptotic performance of estimators of smooth functionals in i.i.d. models. The key idea is to look at a set of local limiting distributions of an estimator sequence, rather than to impose regularity conditions, or to consider limits of maximum risk. Special attention is paid to situations where the tangent cone is not a linear space. As an example, the local asymptotic minimax risk in mixture models is computed.


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Aad van der Vaart. "On the Asymptotic Information Bound." Ann. Statist. 17 (4) 1487 - 1500, December, 1989.


Published: December, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0698.62033
MathSciNet: MR1026295
Digital Object Identifier: 10.1214/aos/1176347377

Primary: 62G20
Secondary: 62C20 , 62F12

Keywords: Asymptotic efficiency , Convolution theorem , local asymptotic minimax risk , local asymptotic normality , mixture model , tangent cone

Rights: Copyright © 1989 Institute of Mathematical Statistics


Vol.17 • No. 4 • December, 1989
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