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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/







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