The Annals of Statistics

Asymptotic equivalence for nonparametric regression with multivariate and random design

Markus Reiß

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

First available in Project Euclid: 16 July 2008

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

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


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.

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