by Mattias Villani
Research Report 1998:6
Department of Statistics, Stockholm University, S-106 91 Stockholm, Sweden
Abstract
A Bayesian analysis of the reduced
rank regression with fixed dimensionality is presented. The relevance of
the model is shown by discussing two of its many encompassed models: MANOVA
and cointegration models.
A normalization is necessary in order
to identify the model and it is shown that different normalizations are
needed for the encompassed models.
The consequences of neglecting the
reduced rank condition in the construction of a diffuse prior are shown
to be severe and a new diffuse prior is derived.
A fully operational and easily implemented
procedure based on Gibbs sampling and Metropolis-Hastings methods is developed
to handle the diffuse analysis based on the new prior.
The diffuse analysis is exemplified
on several simulated and real-world data sets and it seems that the new
diffuse prior overcomes the problem of local non-identification that appeared
in earlier analyses based on priors which did not take the reduced rank
restriction into account.
It is further argued that the special
nature of the model that results from the reduced rank restriction and
the specific applications in which the model is used calls for a discontinous
prior which we model by a finite mixture distribution where some of the
components are Dirac delta functions. The numerical evaluation of the posterior
for the mixture prior is treated and it is shown that parts of the posterior
are analytically tractable.
Key words: Bayesian, Cointegration, MANOVA, Matrix Cauchy, Metropolis-Hastings, Mixture prior, Reduced rank regression.
Last update: 1998-09-28 / KH