English

Exact oracle inequality for a sharp adaptive kernel density estimator

Statistics Theory 2007-06-13 v1 Statistics Theory

Abstract

In one-dimensional density estimation on i.i.d. observations we suggest an adaptive cross-validation technique for the selection of a kernel estimator. This estimator is both asymptotic MISE-efficient with respect to the monotone oracle, and sharp minimax-adaptive over the whole scale of Sobolev spaces with smoothness index greater than 1/2. The proof of the central concentration inequality avoids "chaining" and relies on an additive decomposition of the empirical processes involved.

Keywords

Cite

@article{arxiv.math/0504382,
  title  = {Exact oracle inequality for a sharp adaptive kernel density estimator},
  author = {Clementine Dalelane},
  journal= {arXiv preprint arXiv:math/0504382},
  year   = {2007}
}