Dimension reduction and coefficient estimation in multivariate linear regression

Ming Yuan, Ali Ekici, Zhaosong Lu, Renato Monteiro

Research output: Contribution to journalArticlepeer-review

215 Scopus citations

Abstract

We introduce a general formulation for dimension reduction and coefficient estimation in the multivariate linear model. We argue that many of the existing methods that are commonly used in practice can be formulated in this framework and have various restrictions. We continue to propose a new method that is more flexible and more generally applicable. The method proposed can be formulated as a novel penalized least squares estimate. The penalty that we employ is the coefficient matrix's Ky Fan norm. Such a penalty encourages the sparsity among singular values and at the same time gives shrinkage coefficient estimates and thus conducts dimension reduction and coefficient estimation simultaneously in the multivariate linear model. We also propose a generalized cross-validation type of criterion for the selection of the tuning parameter in the penalized least squares. Simulations and an application in financial econometrics demonstrate competitive performance of the new method. An extension to the non-parametric factor model is also discussed.

Original languageEnglish (US)
Pages (from-to)329-346
Number of pages18
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume69
Issue number3
DOIs
StatePublished - Jun 2007
Externally publishedYes

Keywords

  • Conic programming
  • Dimension reduction
  • Group variable selection
  • Ky Fan norm
  • Penalized likelihood

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