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• W2011283296 abstract "General results on adaptive density estimation are obtained with respect to any countable collection of estimation strategies under Kullback-Leibler and squared $L_2$ losses. It is shown that without knowing which strategy works best for the underlying density, a single strategy can be constructed by mixing the proposed ones to be adaptive in terms of statistical risks. A consequence is that under some mild conditions, an asymptotically minimax-rate adaptive estimator exists for a given countable collection of density classes; that is, a single estimator can be constructed to be simultaneously minimax-rate optimal for all the function classes being considered. A demonstration is given for high-dimensional density estimation on $[0,1]^d$ where the constructed estimator adapts to smoothness and interaction-order over some piecewise Besov classes and is consistent for all the densities with finite entropy." @default.
• W2011283296 created "2016-06-24" @default.
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• W2011283296 date "2000-02-01" @default.
• W2011283296 modified "2023-10-01" @default.
• W2011283296 title "Mixing strategies for density estimation" @default.
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• W2011283296 doi "https://doi.org/10.1214/aos/1016120365" @default.
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