A sharp minimax lower bound for the nonparametric estimation of Sobolev densities of order

Abstract

Results on sharp minimax estimation of the probability density from a Sobolev function class, established in the 1980s, were among the first sharp minimax results in the nonparametric curve estimation literature. This paper considers the last unsolved case -- a Sobolev class of order of densities with infinite support. This brings a closure to this classical topic in the nonparametric curve estimation theory.

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This paper was published in Research Papers in Economics.

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