Technical Working Paper 02-109

Bayesian Bootstrap Multivariate Regression, T. Heckelei and R.C. Mittelhammer May 2002

Abstract

A Bayesian Bootstrap Multivariate Regression (BBMR) procedure is presented that allows robust Bayesian posterior analysis of traditional multivariate regression models. BBMR does not require the specification of a parametric family of the likelihood function and instead uses a bootstrapped likelihood based on the sampling distribution of location and scale estimators. A mixing algorithm for implementing the BBMR procedure automatically incorporates the scale invariant ignorance prior on the covariance matrix. BBMR also allows a flexible choice of prior distributions and can be implemented as a generic algorithm in standard statistical software independently of the actual choice of prior distribution. Monte Carlo evidence is provided showing accuracy and robustness of the approach in representing posterior distributions even under the application of highly non-linear mappings.