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Efficient functional estimation and the super-oracle phenomenon
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Berrett, Thomas B. and Samworth, Richard J. (2023) Efficient functional estimation and the super-oracle phenomenon. Annals of Statistics, 51 (2). pp. 668-690. doi:10.1214/23-AOS2265 ISSN 0090-5364.
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Official URL: https://doi.org/10.1214/23-AOS2265
Abstract
We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide generality, a weighted nearest neighbour estimator is efficient, in the sense of achieving the local asymptotic minimax lower bound. Moreover, we also prove a corresponding central limit theorem, which facilitates the construction of asymptotically valid confidence intervals for the functional, having asymptotically minimal width. One interesting consequence of our results is the discovery that, for certain functionals, the worst-case performance of our estimator may improve on that of the natural ‘oracle’ estimator, which itself can be optimal in the related problem where the data consist of the values of the unknown densities at the observations.
Item Type: | Journal Article | |||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||||||||
Library of Congress Subject Headings (LCSH): | Functions, Entire, Central limit theorem | |||||||||||||||
Journal or Publication Title: | Annals of Statistics | |||||||||||||||
Publisher: | Inst Mathematical Statistics | |||||||||||||||
ISSN: | 0090-5364 | |||||||||||||||
Official Date: | April 2023 | |||||||||||||||
Dates: |
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Volume: | 51 | |||||||||||||||
Number: | 2 | |||||||||||||||
Page Range: | pp. 668-690 | |||||||||||||||
DOI: | 10.1214/23-AOS2265 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
Date of first compliant deposit: | 9 February 2023 | |||||||||||||||
Date of first compliant Open Access: | 28 July 2023 | |||||||||||||||
RIOXX Funder/Project Grant: |
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