Bernstein - von Mises Theorem for growing parameter dimension

Understand

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".