Year: 2013
Type: preprint
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".
Source: arXiv (Cornell University)
Author: Spokoiny, Vladimir
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1602387682