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Alternative procedures to discriminate non nested multivariate linear regression models. (English) Zbl 1072.62050
Summary: This article builds classical and Bayesian testing procedures for choosing between non nested multivariate regression models. Although there are several classical tests for discriminating univariate regressions, only the Cox test is able to consistently handle the multivariate case. We then derive the limiting distribution of the Cox statistic in such a context, correcting an earlier derivation in the literature [see M. H. Pesaran and A. S. Deaton, Econometrica 46, 677–694 (1978; Zbl 0379.62089)]. Further, we show how to build alternative Bayes factors for the testing of nonnested multivariate linear regression models. In particular, we compute expressions for the posterior Bayes factor, the fractional Bayes factor, and the intrinsic Bayes factor.

MSC:
62H15 Hypothesis testing in multivariate analysis
62J05 Linear regression; mixed models
62F15 Bayesian inference
62F03 Parametric hypothesis testing
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