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Optimal correction of an indefinite estimated MA spectral density matrix
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2007 (English)In: Statistics and Probability Letters, ISSN 0167-7152, Vol. 77, no 10, 973-980 p.Article in journal (Refereed) Published
Abstract [en]

Consider a vector moving-average sequence of order n, MA (n), and let Φ (ω) = ∑k = - nn Rk e- j ω k denote its spectral density matrix, where { Rk }k = - nn are the covariance matrices and ω stands for the frequency variable. A nonparametric estimate over(Φ, ^) (ω) = ∑k = - nn over(R, ^)k e- j ω k of Φ (ω) can easily become indefinite at some frequencies, and thus invalid, due to the estimation errors. In this paper, we provide a computationally efficient procedure that obtains the optimal (in a least-squares sense) valid approximation Φ (ω) to over(Φ, ^) (ω) in a polynomial time, by means of a semidefinite programming (SDP) algorithm.

Place, publisher, year, edition, pages
2007. Vol. 77, no 10, 973-980 p.
Keyword [en]
Vector moving-average, Spectral density matrix, Semidefinite programming
National Category
Computer and Information Science
URN: urn:nbn:se:uu:diva-13459DOI: 10.1016/j.spl.2007.01.018ISI: 000246604800005OAI: oai:DiVA.org:uu-13459DiVA: diva2:41229
Available from: 2008-01-23 Created: 2008-01-23 Last updated: 2011-01-31Bibliographically approved

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