Asymptotic equivalence for nonparametric regression with multivariate and random design

2006/07/14 by Markus Reiß, Reiß, Markus · 1 citation
Mathematics · #62B15 #62G08 #62G20 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62B15 #msc:62G08 #msc:62G20 #stat.TH

paper · pdf · doi:10.48550/arxiv.math/0607342

30 pages

arxiv created 2006/07/14 · arxiv updated 2009/12/01

Abstract

We show that nonparametric regression is asymptotically equivalent in Le Cam's sense with 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 permits to achieve asymptotic equivalence even in the cases of multivariate and random design.

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