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  Adaptive wavelet estimation of the diffusion coefficient under additive error measurements.

Hoffmann, M., Munk, A., & Schmidt-Hieber, J. (2012). Adaptive wavelet estimation of the diffusion coefficient under additive error measurements. Annales de l'Institute Henri Poincaré probabilités et statistiques, 48(4), 1186-1216.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000F-9D8D-5 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0027-CA92-E
Genre: Journal Article

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Hoffmann, M., Author
Munk, A.1, Author              
Schmidt-Hieber, J., Author
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1Research Group of Statistical Inverse-Problems in Biophysics, MPI for biophysical chemistry, Max Planck Society, ou_1113580              

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 Abstract: We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular in high frequency financial data modelling, however mainly from a parametric and semiparametric point of view. This paper addresses the nonparametric estimation of the path of the (possibly stochastic) diffusion coefficient in a relatively general setting. By developing pre-averaging techniques combined with wavelet thresholding, we construct adaptive estimators that achieve a nearly optimal rate within a large scale of smoothness constraints of Besov type. Since the diffusion coefficient is usually genuinely random, we propose a new criterion to assess the quality of estimation; we retrieve the usual minimax theory when this approach is restricted to a deterministic diffusion coefficient. In particular, we take advantage of recent results of Reiß (Ann. Statist. 39 (2011) 772–802) of asymptotic equivalence between a Gaussian diffusion with additive noise and Gaussian white noise model, in order to prove a sharp lower bound.

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Language(s): eng - English
 Dates: 2012
 Publication Status: Published online
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 Rev. Method: Peer
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Title: Annales de l'Institute Henri Poincaré probabilités et statistiques
Source Genre: Journal
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Pages: - Volume / Issue: 48 (4) Sequence Number: - Start / End Page: 1186 - 1216 Identifier: -