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July 2007 A complement to Le Cam’s theorem
Mark G. Low, Harrison H. Zhou
Ann. Statist. 35(3): 1146-1165 (July 2007). DOI: 10.1214/009053607000000091


This paper examines asymptotic equivalence in the sense of Le Cam between density estimation experiments and the accompanying Poisson experiments. The significance of asymptotic equivalence is that all asymptotically optimal statistical procedures can be carried over from one experiment to the other. The equivalence given here is established under a weak assumption on the parameter space ℱ. In particular, a sharp Besov smoothness condition is given on ℱ which is sufficient for Poissonization, namely, if ℱ is in a Besov ball Bp,qα(M) with αp>1/2. Examples show Poissonization is not possible whenever αp<1/2. In addition, asymptotic equivalence of the density estimation model and the accompanying Poisson experiment is established for all compact subsets of C([0,1]m), a condition which includes all Hö lder balls with smoothness α>0.


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Mark G. Low. Harrison H. Zhou. "A complement to Le Cam’s theorem." Ann. Statist. 35 (3) 1146 - 1165, July 2007.


Published: July 2007
First available in Project Euclid: 24 July 2007

zbMATH: 1194.62007
MathSciNet: MR2341701
Digital Object Identifier: 10.1214/009053607000000091

Primary: 62G20
Secondary: 62G08

Keywords: additional observations , ‎asymptotic ‎equivalence , decision theory , poissonization

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 3 • July 2007
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