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

Abstract

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.

29 pages

References in corpus (1)

• Uniform asymptotics for kernel density estimators with variable bandwidths

Cited by in corpus (2)

• Central limit theorem for the variable bandwidth kernel density estimators
• Variable bandwidth kernel regression estimation