An extension of cusp estimation problem in ergodic diffusion processes

Takayuki Fujii

Statistics & Probability Letters, 2010, vol. 80, issue 9-10, 779-783

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.

Date: 2010
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