Date of this Version
The Annals of Statistics
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 Bαp,q(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.
asymptotic equivalence, Poissonization, decision theory, additional observations
Low, M. G., & Zhou, H. H. (2007). A Complement to Le Cam’s Theorem. The Annals of Statistics, 35 (3), 1146-1165. http://dx.doi.org/10.1214/009053607000000091
Date Posted: 27 November 2017
This document has been peer reviewed.