Bernstein - von Mises Theorem for growing parameter dimension (1302.3430v4)

Abstract: This paper revisits the prominent Fisher, Wilks, and Bernstein -- von Mises (BvM) results from different viewpoints. Particular issues to address are: nonasymptotic framework with just one finite sample, possible model misspecification, and a large parameter dimension. In particular, in the case of an i.i.d. sample, the mentioned results can be stated for any smooth parametric family provided that the dimension (p ) of the parameter space satisfies the condition "(p^{2}/n ) is small" for the Fisher expansion, while the Wilks and the BvM results require "(p^{3}/n ) is small".