Title: Reduced-Rank Regression: A Dimensionality Reduction Perspective
Abstract: 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 explore the problem of rank estimation from a Dimension Reduction point of view. Connections are established and dimension reduction methodology is applied to estimate both the rank and the predictor subspace that is statistically sufficient for inference on the response vector. We derive an asymptotic test for the rank that only requires the response vector have finite second moments. The test is extended to the non-constant covariance case. Linear combinations of the components of the predictor vector that are estimated to be significant for modelling the responses are obtained.
Seminar to be held in Room 107, 24 Hillhouse at 4:15 pm