Exact oracle inequality for a sharp adaptive kernel density estimator

Details Exact oracle inequality for a sharp adaptive kernel density estimator Exact oracle inequality for a sharp adaptive kernel density estimator

2005-04-19

arxiv.org/abs/math/0504382v1

Mathematics

Statistics Theory

Scientific paper

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.

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