Minimax estimation of the integral of a power of a density

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]<=d/4. We are mostly interested in the case that the power p is larger than 2 and/or the dimension d is large.

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Year of publication:	2008
Authors:	Tchetgen, Eric ; Li, Lingling ; Robins, James ; van der Vaart, Aad
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 78.2008, 18, p. 3307-3311
Publisher:	Elsevier

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005254285