Model-based principal components of covariance matrices
| Autor: | Robert J. Boik, Scott K. Hyde, Kamolchanok Panishkan |
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| Rok vydání: | 2010 |
| Předmět: |
Statistics and Probability
Principal Component Analysis Mathematical optimization Models Statistical Psychometrics Covariance function General Medicine Covariance Edgeworth series Discrepancy function Estimation of covariance matrices Arts and Humanities (miscellaneous) Principal component analysis Confidence Intervals Law of total covariance Humans Applied mathematics Computer Simulation Algorithms General Psychology Eigenvalues and eigenvectors Mathematics |
| Zdroj: | British Journal of Mathematical and Statistical Psychology. 63:113-137 |
| ISSN: | 0007-1102 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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