On the convergence of rank-one multi-target linear regression. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Courrieu, Pierre
• Is Part Of: Statistics. Volume 55:Issue 1(2021)
• Page Start: 68
• Page End: 89
• Publication Date: 2021-01-02
• Subjects: Multi-target linear regression -- multi-output linear regression -- reduced rank multivariate regression -- regression coefficient estimator consistency; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2021.1891236
• Languages: English
• ISSNs: 0233-1888

Abstract

Abstract : This paper presents a new method for solving rank-one multivariate regression problems, providing a solution that maximizes the sum of squared correlations of the one-dimensional fitted pattern with the target variates. The suitability of the method and the consistency of the estimator are formally proved and experimentally tested. In particular, it is shown that the estimate converges not only as a function of the number of items, but also as a function of the number of target variates. An equivalent conventional reduced-rank regression case is identified, and it inherits the convergence properties of the new approach. Application programs in Matlab/Octave code are provided and numerical examples using artificial data as well as real data are presented.