Reduced rank regression analysis provides maximum likelihood estimators of a matrix of regression coefficients of specified rank and of corresponding linear restrictions on such matrices. These estimators depend on the eigenvectors of an ‘‘effect’’ matrix in the metric of an error covariance matrix. In this paper it is shown that the maximum likelihood estimator of the restrictions can be appro...

The present work proposes tests for reduced rank in multivariate regression coefficient matrices, under rather general conditions. A heuristic approach is to first estimate the regressions via standard methods, then compare the coefficient matrix rows (or columns) to assess their redundancy. A formal version of this approach utilizes the distance between an unrestricted coefficient matrix estim...

We propose a new procedure to perform Reduced Rank Regression (RRR) in nonGaussian contexts, based on Multivariate Dispersion Models. Reduced-Rank Multivariate Dispersion Models (RR-MDM) generalise RRR to a very large class of distributions, which include continuous distributions like the normal, Gamma, Inverse Gaussian, and discrete distributions like the Poisson and the binomial. A multivaria...

This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact subset of R. On this approximate eigenbasis the eigenvalues of the covariance function can be expressed as simple functions of the spectral density of the Gau...

In multivariate linear regression, it is often assumed that the response matrix is intrinsically of lower rank. This could be because of the correlation structure among the prediction variables or the coefficient matrix being lower rank. To accommodate both, we propose a reduced rank ridge regression for multivariate linear regression. Specifically, we combine the ridge penalty with the reduced...

Topics in Reduced Rank methods for Multivariate Regression by Ashin Mukherjee Advisors: Professor Ji Zhu and Professor Naisyin Wang Multivariate regression problems are a simple generalization of the univariate regression problem to the situation where we want to predict q(> 1) responses that depend on the same set of features or predictors. Problems of this type is encountered commonly in many...