Asymptotic Expansion of Posterior Distribution of Parameter Centered by a \( \sqrt{n} \)-Consistent Estimate

Abstract

The paper studies asymptotic behavior of posterior distribution of a real parameter centered by a \( \sqrt{n} \)-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.