The Annals of Statistics

Asymptotic equivalence for nonparametric regression with multivariate and random design

Markus Reiß

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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.

Article information

Source
Ann. Statist., Volume 36, Number 4 (2008), 1957-1982.

Dates
First available in Project Euclid: 16 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1216237305

Digital Object Identifier
doi:10.1214/07-AOS525

Mathematical Reviews number (MathSciNet)
MR2435461

Zentralblatt MATH identifier
1142.62023

Subjects
Primary: 62G08: Nonparametric regression 62G20: Asymptotic properties 62B15: Theory of statistical experiments

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

Citation

Reiß, Markus. Asymptotic equivalence for nonparametric regression with multivariate and random design. Ann. Statist. 36 (2008), no. 4, 1957--1982. doi:10.1214/07-AOS525. https://projecteuclid.org/euclid.aos/1216237305


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