Adaptive sequential estimation for ergodic diffusion processes in quadratic metric

L. Galtchouk and S. Pergamenshchikov

Journal of Nonparametric Statistics, 2011, vol. 23, issue 2, 255-285

Abstract: An adaptive nonparametric procedure is constructed for estimating the unknown drift coefficient in ergodic diffusion processes. A sharp non-asymptotic upper bound (an oracle inequality) is obtained for a quadratic risk. Furthermore, an asymptotic lower bound for the minimax quadratic risk is found that equals to the Pinsker constant. Asymptotic efficiency is proved, that is, the asymptotic quadratic risk of the constructed estimator coincides with this constant.

Date: 2011
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Citations: View citations in EconPapers (3)

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DOI: 10.1080/10485252.2010.544307

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