A complement to Le Cam's theorem

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dc.creatorLow, Mark G.
dc.creatorZhou, Harrison H.
dc.date2007-08-16
dc.date.accessioned2026-07-07T08:24:39Z
dc.date.available2026-07-07T08:24:39Z
dc.descriptionThis 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 $\mathcal{F}$. In particular, a sharp Besov smoothness condition is given on $\mathcal{F}$ which is sufficient for Poissonization, namely, if $\mathcal{F}$ is in a Besov ball $B_{p,q}^α(M)$ 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 Hölder balls with smoothness $α>0$.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053607000000091 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0708.2233
dc.identifierhttp://arxiv.org/abs/0708.2233
dc.identifierAnnals of Statistics 2007, Vol. 35, No. 3, 1146-1165
dc.identifierdoi:10.1214/009053607000000091
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136408
dc.subjectStatistics Theory
dc.subject62G20 (Primary); 62G08 (Secondary)
dc.titleA complement to Le Cam's theorem
dc.typetext

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