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December 2014 Asymptotic equivalence for regression under fractional noise
Johannes Schmidt-Hieber
Ann. Statist. 42(6): 2557-2585 (December 2014). DOI: 10.1214/14-AOS1262


Consider estimation of the regression function based on a model with equidistant design and measurement errors generated from a fractional Gaussian noise process. In previous literature, this model has been heuristically linked to an experiment, where the anti-derivative of the regression function is continuously observed under additive perturbation by a fractional Brownian motion. Based on a reformulation of the problem using reproducing kernel Hilbert spaces, we derive abstract approximation conditions on function spaces under which asymptotic equivalence between these models can be established and show that the conditions are satisfied for certain Sobolev balls exceeding some minimal smoothness. Furthermore, we construct a sequence space representation and provide necessary conditions for asymptotic equivalence to hold.


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Johannes Schmidt-Hieber. "Asymptotic equivalence for regression under fractional noise." Ann. Statist. 42 (6) 2557 - 2585, December 2014.


Published: December 2014
First available in Project Euclid: 12 November 2014

zbMATH: 1302.62097
MathSciNet: MR3277671
Digital Object Identifier: 10.1214/14-AOS1262

Primary: 62G08
Secondary: 62G20

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 6 • December 2014
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