Regularised covariance matrix estimation under the common principal components model

Pepler, P.T. , Uys, D.W. and Nel, D.G. (2018) Regularised covariance matrix estimation under the common principal components model. Communications in Statistics: Simulation and Computation, 47(3), pp. 631-643. (doi: 10.1080/03610918.2015.1040499)

Abstract

The common principal components (CPC) model provides a way to model the population covariance matrices of several groups by assuming a common eigenvector structure. When appropriate, this model can provide covariance matrix estimators of which the elements have smaller standard errors than when using either the pooled covariance matrix or the per group unbiased sample covariance matrix estimators. In this paper, a regularised CPC estimator under the assumption of a common (or partially common) eigenvector structure in the populations is proposed. After estimation of the common eigenvectors using the Flury-Gautschi (or other) algorithm, the off-diagonal elements of the nearly diagonalised covariance matrices are shrunk towards zero and multiplied with the orthogonal common eigenvector matrix to obtain the regularised CPC covariance matrix estimates. The optimal shrinkage intensity per group can be estimated using cross-validation. The efficiency of these estimators compared to the pooled and unbiased estimators is investigated in a Monte Carlo simulation study, and the regularised CPC estimator is applied to a real data set to demonstrate the utility of the method.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Pepler, Dr Theo
• Authors: Pepler, P.T., Uys, D.W., and Nel, D.G.
• College/School: College of Medical Veterinary and Life Sciences > School of Biodiversity, One Health & Veterinary Medicine
• Journal Name: Communications in Statistics: Simulation and Computation
• Publisher: Taylor & Francis
• ISSN: 0361-0918
• ISSN (Online): 1532-4141
• Published Online: 10 June 2015