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Likelihood ratio tests for model selection and non-nested hypotheses

Vuong, Quang H. (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57 (2). pp. 307-333. ISSN 0012-9682. doi:10.2307/1912557.

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In this paper, we develop a classical approach to model selection. Using the Kullback-Leibler Information Criterion to measure the closeness of a model to the truth, we propose simple likelihood-ratio based statistics for testing the null hypothesis that the competing models are equally close to the true data generating process against the alternative hypothesis that one model is closer. The tests are directional and are derived successively for the cases where the competing models are non-nested, overlapping, or nested and whether both, one, or neither is misspecified. As a prerequisite, we fully characterize the asymptotic distribution of the likelihood ratio statistic under the most general conditions. We show that it is a weighted sum of chi-square distribution or a normal distribution depending on whether the distributions in the competing models closest to the truth are observationally identical. We also propose a test of this latter condition.

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Additional Information:© 1989 Econometric Society. This research was supported by National Science Foundation Grant SES-8410593. An early version was presented at the North American Econometric Society meeting, New Orleans, 1986. I am indebted to P. Bjorn, D. Lien, D. Rivers, the co-editor, two referees, and seminar participants at the University of Southern California, University of California-Berkeley, Stanford University, University of Minnesota, University of Wisconsin, Yale University, MIT/Harvard University, University of Pennsylvania, University of Florida-Gainesville, North Carolina State/Duke University, Indiana University, and University of California-Irvine. I would like to thank especially H. White whose comments much improved this paper. I am grateful to C. R. Jackson and to L. Donnelly for stimulating thoughts. Remaining errors are mine. This paper is dedicated to some of my former colleagues at Caltech. Formerly SSWP 605.
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Subject Keywords:Likelihood ratio tests, model selection, non-nested hypotheses, misspecified models, weighted sums of chi-squares.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83161
Deposited By: Jacquelyn Bussone
Deposited On:16 Nov 2017 00:24
Last Modified:15 Nov 2021 19:55

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