Geodesic
Likelihood ratio for densities with singularity
Zapiski Nauchnykh Seminarov POMI, Studies in the statistical estimation theory. Part I, Tome 74 (1977), pp. 66-82

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Let $t_n$ be Bayes estimate of parameter $\Theta$. The case of independent observations with infinite information quantity is considered. Under some conditions on densities it is shown that normalizing factor $\varphi(n)$ for $\Delta_n\varphi(n)(t_n-\Theta)$ to have nontrivial asymptotic destribution is regularly changing in the sence of Karamata. Asymptotic distribution of $\Delta_n$ derived. 
@article{ZNSL_1977_74_a1,
     author = {N. K. Bakirov},
     title = {Likelihood ratio for densities with singularity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {66--82},
     publisher = {mathdoc},
     volume = {74},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_74_a1/}
}
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N. K. Bakirov. Likelihood ratio for densities with singularity. Zapiski Nauchnykh Seminarov POMI, Studies in the statistical estimation theory. Part I, Tome 74 (1977), pp. 66-82. http://geodesic.mathdoc.fr/item/ZNSL_1977_74_a1/