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

On the estimation of smooth densities by strict probability densities at optimal rates in sup-norm - Mathematics > Statistics Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: It is shown that the variable bandwidth density estimator proposed by McKay1993a and b following earlier findings by Abramson 1982 approximatesdensity functions in \$C^4\mathbb R^d\$ at the minimax rate in the supremumnorm over bounded sets where the preliminary density estimates on which theyare based are bounded away from zero. A somewhat more complicated estimatorproposed by Jones McKay and Hu 1994 to approximate densities in \$C^6\mathbbR\$ is also shown to attain minimax rates in sup norm over the same kind ofsets. These estimators are strict probability densities.

Author: Evarist Giné, Hailin Sang

Source: https://arxiv.org/