Asymptotic equivalence for nonparametric regression with multivariate and random design
Open Access
- 1 August 2008
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 36 (4) , 1957-1982
- https://doi.org/10.1214/07-aos525
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.Keywords
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This publication has 15 references indexed in Scilit:
- Asymptotic statistical equivalence for ergodic diffusions: the multidimensional caseProbability Theory and Related Fields, 2006
- Random Sampling of Multivariate Trigonometric PolynomialsSIAM Journal on Mathematical Analysis, 2005
- Equivalence theory for density estimation, Poisson processes and Gaussian white noise with driftThe Annals of Statistics, 2004
- Boundary coiflets for wavelet shrinkage in function estimationJournal of Applied Probability, 2004
- Asymptotic equivalence theory for nonparametric regression with random designThe Annals of Statistics, 2002
- Random rates in anisotropic regression (with a discussion and a rejoinder by the authors)The Annals of Statistics, 2002
- Asymptotic equivalence for nonparametric generalized linear modelsProbability Theory and Related Fields, 1998
- Asymptotic nonequivalence of nonparametric experiments when the smoothness index is ½The Annals of Statistics, 1998
- Asymptotic equivalence of density estimation and Gaussian white noiseThe Annals of Statistics, 1996
- Asymptotic equivalence of nonparametric regression and white noiseThe Annals of Statistics, 1996