Article ID Journal Published Year Pages File Type
10524749 Journal of Multivariate Analysis 2005 13 Pages PDF
Abstract
Let f be an unknown multivariate density belonging to a prespecified parametric class of densities, Fk, where k is unknown, but Fk⊂Fk+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,k̂ with the property that E{∫|fn,k̂−f|}=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.
Related Topics
Physical Sciences and Engineering Mathematics Numerical Analysis
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