Multivariate Reduced Rank Regression in Non-Gaussian Contexts, Using Copulas
CORE Discussion Paper No. 2004/32
14 Pages Posted: 31 Mar 2007
Date Written: May 2004
We propose a new procedure to perform Reduced Rank Regression (RRR) in non-Gaussian contexts, based on Multivariate Dispersion Models. Reduced-Rank Multivariate Dispersion Models (RR-MDM) generalise RRR to a very large class of distributions, which include continuous distributions like the normal, Gamma, Inverse Gaussian, and discrete distributions like the Poisson and the binomial. A mul-tivariate distribution is created with the help of the Gaussian copula and estimation is performed using maximum likelihood. We show how this method can be amended to deal with the case of discrete data. We perform Monte Carlo simulations and show that our estimator is more efficient than the traditional Gaussian RRR. In the framework of MDM's we introduce a procedure analogous to canonical correlations, which takes into account the distribution of the data.
Keywords: multivariate dispersion model, multivariate statistical analysis, canonical correlations, principal component analsysis
JEL Classification: C35, C39
Suggested Citation: Suggested Citation