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June 2000 Adaptive drift estimation for nonparametric diffusion model
Vladimir G. Spokoiny
Ann. Statist. 28(3): 815-836 (June 2000). DOI: 10.1214/aos/1015951999

Abstract

We consider a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. The goal is to estimate the unknown drift coefficient.We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and nearly optimal up to a log log factor. The results about the quality of estimation are nonasymptotic and do not require any ergodic or mixing properties of the observed process.

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Vladimir G. Spokoiny. "Adaptive drift estimation for nonparametric diffusion model." Ann. Statist. 28 (3) 815 - 836, June 2000. https://doi.org/10.1214/aos/1015951999

Information

Published: June 2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62330
MathSciNet: MR1792788
Digital Object Identifier: 10.1214/aos/1015951999

Subjects:
Primary: 62G05
Secondary: 62M99

Keywords: Bandwidth selection , Drift and diffusion coefficients , nonparametric estimation

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 3 • June 2000
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