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Adaptive sequential estimation for ergodic diffusion processes in quadratic metric

Author

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  • L. Galtchouk
  • S. Pergamenshchikov

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.

Suggested Citation

  • L. Galtchouk & S. Pergamenshchikov, 2011. "Adaptive sequential estimation for ergodic diffusion processes in quadratic metric," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 255-285.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:255-285
    DOI: 10.1080/10485252.2010.544307
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    Cited by:

    1. Leonid I. Galtchouk & Serge M. Pergamenshchikov, 2022. "Adaptive efficient analysis for big data ergodic diffusion models," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 127-158, April.
    2. Mayerhofer, Eberhard & Stelzer, Robert & Vestweber, Johanna, 2020. "Geometric ergodicity of affine processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4141-4173.
    3. Galtchouk, L. & Pergamenshchikov, S., 2013. "Uniform concentration inequality for ergodic diffusion processes observed at discrete times," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 91-109.

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