Title: Bootstrapping for multivariate linear regression models,
Abstract: The multivariate linear regression model is an important tool for
investigating relationships between several response variables and several
predictor variables. The primary interest is in inference about the unknown
regression coefficient matrix. We propose multivariate bootstrap techniques as
a means for making inferences about the unknown regression coefficient matrix.
These bootstrapping techniques are extensions of those developed in Freedman
(1981), which are only appropriate for univariate responses. Extensions to the
multivariate linear regression model are made without proof. We formalize this
extension and prove its validity. A real data example and two simulated data
examples which offer some finite sample verification of our theoretical results
are provided.