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An extension of cusp estimation problem in ergodic diffusion processes

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  • Fujii, Takayuki

Abstract

We consider a non-regular estimation problem in ergodic diffusion processes whose drift coefficient includes a component x-[theta]p with . This is an extension of the work of Dachian and Kutoyants (2003) that deals with the case . We study the asymptotic behavior of the Bayes estimator via Ibragimov and Khasminskii's approach. Its convergence rate and asymptotic distribution are given. Furthermore, the Bayes estimator is asymptotically efficient in a certain minimax sense.

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  • Fujii, Takayuki, 2010. "An extension of cusp estimation problem in ergodic diffusion processes," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 779-783, May.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:9-10:p:779-783
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    Cited by:

    1. O. V. Chernoyarov & S. Dachian & Yu. A. Kutoyants, 2018. "On parameter estimation for cusp-type signals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 39-62, February.
    2. Kordzakhia, Nino E. & Kutoyants, Yury A. & Novikov, Alexander A. & Hin, Lin-Yee, 2018. "On limit distributions of estimators in irregular statistical models and a new representation of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 141-151.
    3. S. Dachian & N. Kordzakhia & Yu. A. Kutoyants & A. Novikov, 2018. "Estimation of cusp location of stochastic processes: a survey," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 345-362, July.

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