A complement to Le Cam’s theorem
Low, Mark G. ; Zhou, Harrison H.
Ann. Statist., Tome 35 (2007) no. 1, p. 1146-1165 / Harvested from Project Euclid
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.
Publié le : 2007-07-14
Classification:  Asymptotic equivalence,  Poissonization,  decision theory,  additional observations,  62G20,  62G08
@article{1185304001,
     author = {Low, Mark G. and Zhou, Harrison H.},
     title = {A complement to Le Cam's theorem},
     journal = {Ann. Statist.},
     volume = {35},
     number = {1},
     year = {2007},
     pages = { 1146-1165},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1185304001}
}
Low, Mark G.; Zhou, Harrison H. A complement to Le Cam’s theorem. Ann. Statist., Tome 35 (2007) no. 1, pp.  1146-1165. http://gdmltest.u-ga.fr/item/1185304001/