Geodesic
Asymptotic expansion of posterior distribution of parameter centered by a~$\sqrt n$-consistent estimate
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 121-150

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The article studies asymptotic behaviour of posterior distribution of a real parameter centered by a $\sqrt n$-consistent estimate. An analogue of Bernstein–von Mises theorem is presented. The article emphasizes uniformity of the result. In the same framework asymptotic expansions of posterior distribution and posterior mean of functions bounded by polynomial are constructed. 
@article{ZNSL_2016_454_a6,
     author = {A. A. Zaikin},
     title = {Asymptotic expansion of posterior distribution of parameter centered by a~$\sqrt n$-consistent estimate},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {121--150},
     publisher = {mathdoc},
     volume = {454},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a6/}
}
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A. A. Zaikin. Asymptotic expansion of posterior distribution of parameter centered by a~$\sqrt n$-consistent estimate. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 121-150. http://geodesic.mathdoc.fr/item/ZNSL_2016_454_a6/