Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density

This paper is a continuation of author's paper [I]. Like [I] we consider here a sample $(x_1,\dots,x_n)$ with common density $f(x-\Theta)$ depending on unknown parameter $\Theta$. It is supposed that $f$ is sufficiently smooth exept the finite set of points of singularity of the form (1.1).
The main result asserts that for Bayesian estimates $\hat{t}_n$ random variables $n^{1/1+\alpha}(\hat{t}_n-\Theta)$ has a proper limit distribution where $\alpha$ is from (1.1).