Cholesky Decompositions and Estimation of A Covariance Matrix: Orthogonality of Variance--Correlation Parameters

Mohsen Pourahmadi

Biometrika, 2007, vol. 94, issue 4, 1006-1013

Abstract: Chen & Dunson ([3]) have proposed a modified Cholesky decomposition of the form σ = D L L′D for a covariance matrix where D is a diagonal matrix with entries proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix solely determining its correlation matrix. This total separation of variance and correlation is definitely a major advantage over the more traditional modified Cholesky decomposition of the form LD-super-2L′, (Pourahmadi, [13]). We show that, though the variance and correlation parameters of the former decomposition are separate, they are not asymptotically orthogonal and that the estimation of the new parameters could be more demanding computationally. We also provide statistical interpretation for the entries of L and D as certain moving average parameters and innovation variances and indicate how the existing likelihood procedures can be employed to estimate the new parameters. Copyright 2007, Oxford University Press.

Date: 2007
References: Add references at CitEc
Citations: View citations in EconPapers (18)

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asm073 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:94:y:2007:i:4:p:1006-1013

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().