Geodesic
Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 3, Tome 55 (1976), pp. 175-184 Cet article a éte moissonné depuis la source Math-Net.Ru

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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). 
@article{ZNSL_1976_55_a10,
     author = {I. A. Ibragimov and R. Z. Khas'minskii},
     title = {Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {175--184},
     year = {1976},
     volume = {55},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_55_a10/}
}
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I. A. Ibragimov; R. Z. Khas'minskii. Asymptotic behavior of statistical estimates of the shift parameter for samples with unbounded density. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part 3, Tome 55 (1976), pp. 175-184. http://geodesic.mathdoc.fr/item/ZNSL_1976_55_a10/