Principal component models for correlation matrices

Robert J. Boik

Biometrika, 2003, vol. 90, issue 3, 679-701

Abstract: Distributional theory regarding principal components is less well developed for correlation matrices than it is for covariance matrices. The intent of this paper is to reduce this disparity. Methods are proposed that enable investigators to fit and to make inferences about flexible principal components models for correlation matrices. The models allow arbitrary eigenvalue multiplicities and allow the distinct eigenvalues to be modelled parametrically or nonparametrically. Local parameterisations and implicit functions are used to construct full-rank unconstrained parameterisations. First-order asymptotic distributions are obtained directly from the theory of estimating functions. Second-order accurate distributions for making inferences under normality are obtained directly from likelihood theory. Simulation studies show that the Bartlett correction is effective in controlling the size of the tests and that first-order approximations to nonnull distributions are reasonably accurate. The methods are illustrated on a dataset. Copyright Biometrika Trust 2003, Oxford University Press.

Date: 2003
References: Add references at CitEc
Citations: View citations in EconPapers (7)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:90:y:2003:i:3:p:679-701

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 ().