Consistent Bayesian information criterion based on a mixture prior for possibly high-dimensional multivariate linear regression models |
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Authors: | Haruki Kono Tatsuya Kubokawa |
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Institution: | 1. Department of Economics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA;2. Department of Economics, University of Tokyo, Tokyo, Japan |
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Abstract: | In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC). Inheriting their asymptotic properties, our information criteria are consistent in variable selection in both the large-sample and the high-dimensional asymptotic frameworks. In numerical simulations, variable selection methods based on our information criteria choose the true set of variables with high probability in most cases. |
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Keywords: | consistency high-dimensional data information criterion mixture distribution multivariate linear regression variable selection |
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