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August 2008 Asymptotic equivalence for nonparametric regression with multivariate and random design
Markus Reiß
Ann. Statist. 36(4): 1957-1982 (August 2008). DOI: 10.1214/07-AOS525

Abstract

We show that nonparametric regression is asymptotically equivalent, in Le Cam’s sense, to a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework, based on approximation spaces, which allows asymptotic equivalence to be achieved, even in the cases of multivariate and random design.

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Markus Reiß. "Asymptotic equivalence for nonparametric regression with multivariate and random design." Ann. Statist. 36 (4) 1957 - 1982, August 2008. https://doi.org/10.1214/07-AOS525

Information

Published: August 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1142.62023
MathSciNet: MR2435461
Digital Object Identifier: 10.1214/07-AOS525

Subjects:
Primary: 62B15 , 62G08 , 62G20

Keywords: approximation space , equivalence of experiments , Gaussian white noise , interpolation , Le Cam deficiency

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 4 • August 2008
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