2007/07/01 by Mark G. Low, Harrison H. Zhou · 1 citation
Economics, Econometrics and Finance · Mathematics · #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Stochastic processes and financial applications #math.ST #msc:62G08 #msc:62G20 #stat.TH
paper · pdf · doi:10.1214/009053607000000091
published as Annals of Statistics 2007, Vol. 35, No. 3, 1146-1165 · Published 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)
openalex publication_date 2007/07/01 · arxiv created 2007/08/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.