An extension of cusp estimation problem in ergodic diffusion processes

We consider a non-regular estimation problem in ergodic diffusion processes whose drift coefficient includes a component |x−θ|p with p∈(−12,0). This is an extension of the work of Dachian and Kutoyants (2003) that deals with the case p∈(0,12). 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.