Reduced rank regression assumes that the coefficient matrix in a multivariate regression model is not of full rank. The unknown rank is traditionally estimated under the assumption of normal responses. We derive an asymptotic test for the rank that only requires the response vector have finite second moments. The test is extended to the nonconstant covariance case. Linear combinations of the components of the predictor vector that are estimated to be significant for modelling the responses are obtained.
Bibliographical noteFunding Information:
We would like to thank two anonymous referees and T.W. Anderson for valuable comments and for familiarizing us with relevant work. Their suggestions improved this article significantly. The first author would also like to thank the National Science Foundation and Ingram Olkin (DMS-9631278) for giving her the opportunity to visit the Department of Statistics at Stanford during the summer of 2001 where most of this work was completed. She was also supported by the National Foundation Grant DMS-0204563. The second author's work was supported in part by National Science Foundation Grants DMS-9703777 and DMS-0103983.
- Asymptotic test
- Weighted chi-squared