This paper presents a procedure for coefficient estimation in a multivariate regression model of reduced rank in the presence of multicollinearity. The procedure permits the prediction of the dependent variables taking advantage of both Partial Least Squares (PLS) and Singular Value Decomposition (SVD) methods, which is denoted by PLSSVD. Global variability indices and prediction error sums are...

Many modern statistical problems can be cast in the framework of multivariate regression, where the main task is to make statistical inference for a possibly sparse and low-rank coefficient matrix. The low-rank structure in the coefficient matrix is of intrinsic multivariate nature, which, when combined with sparsity, can further lift dimension reduction, conduct variable selection, and facilit...

In functional data analysis (FDA) it is of interest to generalize techniques of multivariate analysis like canonical correlation analysis or regression to functions which are often observed with noise. In the proposed Bayesian approach to FDA two tools are combined: (i) a special Demmler-Reinsch like basis of interpolation splines to represent functions parsimoniously and ‡exibly; (ii) latent v...

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The problem is formulated to minimize the least squares loss with a sparsity-inducing penalty considering an orthogonality constraint. Convex sparsity-inducing ...

Reduced-rank regression, i.e., multi-task regression subject to a low-rank constraint, is an effective approach to reduce the number of observations required for estimation consistency. However, it is still possible for the estimated singular vectors to be inconsistent in high dimensions as the number of predictors go to infinity with a faster rate than the number of available observations. Spa...