On the estimation of smooth densities by strict probability densities at optimal rates in sup-norm

Details On the estimation of smooth densities by strict probability densities at optimal rates in sup-norm On the estimation of smooth densities by strict probability densities at optimal rates in sup-norm

2010-06-04

arxiv.org/abs/1006.0971v3

Mathematics

Statistics Theory

29 pages

Scientific paper

It is shown that the variable bandwidth density estimator proposed by McKay (1993a and b) following earlier findings by Abramson (1982) approximates density functions in $C^4(\mathbb R^d)$ at the minimax rate in the supremum norm over bounded sets where the preliminary density estimates on which they are based are bounded away from zero. A somewhat more complicated estimator proposed by Jones McKay and Hu (1994) to approximate densities in $C^6(\mathbb R)$ is also shown to attain minimax rates in sup norm over the same kind of sets. These estimators are strict probability densities.

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