We propose an approach to the regularization of covariance matrices that can be applied to any model for which the likelihood is available in closed form. The approach is based on using mixtures of double exponential or normal distributions as priors for correlation parameters, and on maximizing the resulting log-posterior (or penalized likelihood) using a stochastic optimization algorithm. The mixture priors are capable of clustering the correlations in several groups, each with separate mean and variance, and can therefore capture a large variety of structures besides sparsity. We apply this approach to the traditional normal regression model as well as to several other models of interest to financial decision making that have not been previously studied for the purpose of regularization, including multivariate t, normal and t copulas, and mixture of normal distributions. Simulation experiments show the potential for large efficiency gains in all these models. Sizable gains also arise in two empirical applications; A Fama-French three-factor model for industry returns (30 assets), and a vector autoregression model for realized volatilities (19 assets). This is a joint work with Paolo Giordani, Research Division, Swedish Central Bank and Xiuyan Mun, Australian School of Business, UNSW.  

About the speaker: Robert Kohn is Scientia Professor at the Australian School of Business at the University of New South Wales. His research activities concentrate on Statistics and Econometrics. His wide expertise covers Bayesian methodology, variable selection problems, nonparametric regression for both Gaussian and non-Gaussian models, covariance selection and time series models.


Professor Robert Kohn

Research Area

Statistics Seminar


Australian School of Business, UNSW


Fri, 07/05/2010 - 4:00pm