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Maximum likelihood parameter and rank estimation in reduced-rank multivariate linear regressions
Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology. Uppsala University, Teknisk-naturvetenskapliga vetenskapsområdet, Mathematics and Computer Science, Department of Information Technology, Automatic control.
1996 (English)In: IEEE TRANSACTIONS ON SIGNAL PROCESSING, ISSN 1053-587X, Vol. 44, no 12, 3069-3078 p.Article in journal (Refereed) Published
Abstract [en]

This paper considers the problem of maximum likelihood (ML) estimation for reduced-rank linear regression equations with noise of arbitrary covariance. The rank-reduced matrix of regression coefficients is parameterized as the product of two full-rank factor matrices. This parameterization is essentially constraint free, but it is not unique, which renders the associated ML estimation problem rather nonstandard. Nevertheless, the problem turns out to be tractable, and the following results are obtained. An explicit expression is derived for the ML estimate of the regression matrix in terms of the data covariances and their eigenelements. Furthermore, a detailed analysis of the statistical properties of the ML parameter estimate is performed. Additionally, a generalized likelihood ratio test (GLRT) is proposed for estimating the rank of the regression matrix. The paper also presents the results of some simulation exercises, which lend empirical support to the theoretical findings

Place, publisher, year, edition, pages
1996. Vol. 44, no 12, 3069-3078 p.
Identifiers
URN: urn:nbn:se:uu:diva-27214OAI: oai:DiVA.org:uu-27214DiVA: diva2:55108
Note
Addresses: Stoica P, UNIV UPPSALA, SYST & CONTROL GRP, BOX 27, S-75103 UPPSALA, SWEDEN. CHALMERS UNIV TECHNOL, DEPT APPL ELECT, S-41296 GOTHENBURG, SWEDEN.Available from: 2007-02-09 Created: 2007-02-09 Last updated: 2011-01-15

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http://ieeexplore.ieee.org/iel4/78/12011/00553480.pdf?isnumber=12011&prod=JNL&arnumber=553480&arSt=3069&ared=3078&arAuthor=Stoica%2C+P.%3B+Viberg%2C+M.

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