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arXiv 2010-06-04 DOI 10.1214/12-IMSCOLL910 0 views

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

Giné, Evarist · Sang, Hailin

Original · EN

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 C⁴(Rᵈ) 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 C⁶(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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