The likelihood ratio for densities with singularities

Let t_n be the Bayesian estimator of the parameter constructed from independent observations in the case of infinite information and probability distribution density with some singularities. It is shown that under certain conditions on the behavior of the densities near their singularities, the normalizing factor (n) ensuring that _n=(n) (t_n-) has a nontriviallimiting distribution for n is regularly varying in Karamata's sense. The limiting distribution of _n is determined.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 74, pp. 66–82, 1977.I would like to acknowledge the guidance of I. A. Ibragimov in the course of this research.