Asymptotic Expansion of Posterior Distribution of Parameter Centered by a √n -Consistent Estimate

Abstract

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. The paper studies asymptotic behavior of posterior distribution of a real parameter centered by a n-consistent estimate. The uniform analog of the Bernstein–von Mises theorem is proved. This result is extended to asymptotic expansion of the posterior distribution in powers of n−1/2. This expansion is generalized as the expansion of expectations of functions with polynomial majorant with respect to posterior distribution.