Asymptotic behavior of the joint distribution of a vector of stochastically dependent likelihood ratios

TL;DR

This paper generalizes Wilks' classical result by analyzing the asymptotic behavior of the joint distribution of a vector of stochastically dependent likelihood ratios, extending understanding of their joint asymptotic properties.

Contribution

It introduces new asymptotic results for the joint distribution of dependent likelihood ratios, broadening the classical Wilks' theorem framework.

Findings

Derived the asymptotic distribution for dependent likelihood ratio vectors

Extended Wilks' theorem to multivariate dependent cases

Provided theoretical insights into joint likelihood ratio behavior

Abstract

This paper provides a generalization of a classical result obtained by Wilks about the asymptotic behavior of the likelihood ratio. The new results deal with the asymptotic behavior of the joint distribution of a vector of likelihood ratios which turn out to be stochastically dependent.