Bayesian Assessment of Dimensionality in Multivariate Reduced Rank Regression

Jukka Corander and Mattias Villani

Abstract
We consider Bayesian inference about the dimensionality in the multivariate reduced rank regression framework, which encompasses several models such as MANOVA, simultaneous equations, factor analysis and cointegration models for multiple time series. The fractional Bayes approach is used to derive an approximation to the posterior distribution of the dimensionality. To investigate the finite sample properties of our solution, we have applied it to a wide variety of real and simulated data sets. The proposed approach compares favorably to other established estimators of the dimensionality.

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