Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10524749 | Journal of Multivariate Analysis | 2005 | 13 Pages |
Abstract
Let f be an unknown multivariate density belonging to a prespecified parametric class of densities, Fk, where k is unknown, but FkâFk+1 for all k and each Fk has finite Vapnik-Chervonenkis dimension. Given an i.i.d. sample of size n drawn from f, we show that it is possible to select automatically, and without extra restrictions on f, an estimate fn,kÌ with the property that E{â«|fn,kÌâf|}=O(1/n). Our method is inspired by the combinatorial tools developed in Devroye and Lugosi (Combinatorial Methods in Density Estimation, Springer, New York, 2001) and it includes a wide range of density models, such as mixture models or exponential families.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Numerical Analysis
Authors
Gérard Biau, Luc Devroye,