Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses

(1989) - Quang H. Vuong

Journal: Econometrica
Link:: https://www.jstor.org/stable/1912557?origin=crossref
DOI:: 10.2307/1912557
Links::
Tags:: #paper #Methods #Hausman-Mcfadden #likelihood
Cite Key:: [@vuongLikelihoodRatioTests1989]

Abstract

In this paper , we propose a classical approach to model selection. Using the Kullback-Leibler Information measur e , we propose simple and directional likelihood-ratio tests for discriminating and choosing between two compe ting models whether the model s are non­ nested , overlapping or nested and whether both, one, or nei ther is misspecified. As a prerequisite, we ful ly characterize the asym ptotic distribution of the likelihood ratio statistic under the most general conditi ons.

Notes

“Since Neyman and Pearson (1928) advocated the LR test, it has become one of the most popular methods for testing restrictions on the parameters of a statistical model. It is well-known that minus twice the LR statistic has a limitin g central chi-square distribution under the null hypothesis (Wilks (1938)), and a limiting non-central chisquare distribution under a sequence of local alternatives (Wald (1943)) with a non-ce ntrality parameter equal to that of the Wald statistic (Wald (1943)) and Lagrange Multiplier statistic (Aitchinson and Silvey (1958) , Silvey (1959)” (Vuong, 1989, p. 4)