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Aspects of common principal components
Jönköping University, Jönköping International Business School, JIBS, Statistics.
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The focus of this thesis is the common principal component (CPC) model, the generalization of principal components to several populations. Common principal components refer to a group of multidimensional datasets such that their inner products share the same eigenvectors and are therefore simultaneously diagonalized by a common decorrelator matrix. Common principal component analysis is essentially applied in the same areas and analysis as its one-population counterpart. The generalization to multiple populations comes at the cost of being more mathematically involved, and many problems in the area remains to be solved.

This thesis consists of three individual papers and an introduction chapter.In the first paper, the performance of two different estimation methods of the CPC model is compared for two real-world datasets and in a Monte Carlo simulation study. The second papers show that the orthogonal group and the Haar measure on this group plays an important role in PCA, both in single- and multi-population principal component analysis. The last paper considers using common principal component analysis as a tool for imposing restrictions on system-wise regression models. When the exogenous variables of a multi-dimensional model share common principal components, then each of the marginal models in the system is, up to their eigenvalues, identical. They henceform a class of regression models situated in between the classical seemingly unrelated regressions, where each set of explanatory variables is unique, and multivariate regression, where each marginal model shares the same common set of regressors.

Place, publisher, year, edition, pages
Jönköping: Jönköping University, Jönköping International Business School , 2017. , p. 80
Series
JIBS Research Reports, ISSN 1403-0462 ; 2017-2
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hj:diva-38587ISBN: 978-91-86345-79-2 (print)OAI: oai:DiVA.org:hj-38587DiVA, id: diva2:1175063
Supervisors
Available from: 2018-01-17 Created: 2018-01-17 Last updated: 2018-01-17Bibliographically approved
List of papers
1. A comparison of two estimation methods of the common principal component model
Open this publication in new window or tab >>A comparison of two estimation methods of the common principal component model
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:hj:diva-38578 (URN)
Available from: 2018-01-17 Created: 2018-01-17 Last updated: 2018-01-17
2. A small excursion on the Haar measure on Op
Open this publication in new window or tab >>A small excursion on the Haar measure on Op
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:hj:diva-38584 (URN)
Available from: 2018-01-17 Created: 2018-01-17 Last updated: 2018-01-17
3. Common principal components with applications in regression
Open this publication in new window or tab >>Common principal components with applications in regression
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:hj:diva-38586 (URN)
Available from: 2018-01-17 Created: 2018-01-17 Last updated: 2018-01-17

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Duras, Toni

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