Introduction to High-Dimensional Statistics, 2nd Edition

Chapter 8

Multivariate Regression

DOI: 10.1201/9781003158745-8

In the previous chapters, we have focused on a response y that was 1-dimensional. In many cases, we do not focus on a single quantity y ∈ ℝ, but rather on a T-dimensional vector y = (y₁,...,y_T) ∈ ℝ^T of measurements. It is, of course, possible to analyze each coordinate y_t independently, but it is usually wise to analyze simultaneously the T coordinates y₁,...,y_T. Actually, when y₁,..., y_T are the outcome of a common process, they usually share some common structures, and handling the T measurements y₁,...,y_T together enables to rely on these structures.

In this chapter, we give a special focus on the case where the measurements lie in the vicinity of an (unknown) low-dimensional ...