Minimax estimation of the integral of a power of a density

Eric Tchetgen, Lingling Li, James Robins and Aad van der Vaart

Statistics & Probability Letters, 2008, vol. 78, issue 18, 3307-3311

Abstract: We construct an estimator of , based on a random sample of size n from a density f on the unit cube in . This estimator achieves the minimax rate for f known to belong to a multiple of the unit ball in a Hölder space of order [alpha], where [alpha]

Date: 2008
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