Asymptotic equivalence for nonparametric regression with multivariate and random design
Markus Reiß
Source: Ann. Statist. Volume 36, Number 4 (2008), 1957-1982.
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.
Primary Subjects: 62G08, 62G20, 62B15
Keywords: Le Cam deficiency; equivalence of experiments; approximation space; interpolation; Gaussian white noise
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1216237305
Digital Object Identifier: doi:10.1214/07-AOS525
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