title: Model-based principal components of covariance matrices.
abstract: A flexible class of models is proposed for principal component (PCs) of covariance matrices. The models allow constraints to be imposed on the eigenvalues and/or the eigenvectors and yield simplified PCs that retain their variance maximization and orthogonality properties. The models are fitted to sample covariance matrices by minimizing a discrepancy function. Asymptotic distributions of estimators are obtained under the assumption that fourth-order moments of the parent distribution are finite. Hypothesis tests are obtained by comparing discrepancy functions that are minimized under different constraints. An Edgeworth expansion is used to obtain second-order accurate confidence intervals for differentiable eigenfunctions. The techniques are illustrated on a real data set.
authors.affiliation: Department of Mathematical Sciences, Montana State University, Bozeman, Montana, USA. rjboik@math.montana.edu
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Boik
authors.forename: Kamolchanok
authors.initials: K
authors.lastname: Panishkan
authors.forename: Scott K
authors.initials: SK
authors.lastname: Hyde
mesh_terms: D000465:Algorithms; D003198:Computer Simulation / Q000706:statistics & numerical data; D016001:Confidence Intervals; D006801:Humans; D015233:Models, Statistical; D025341:Principal Component Analysis / Q000379:methods*; D011594:Psychometrics / Q000706:statistics & numerical data*