In many real datasets, the same variables are measured on objects from different groups, and the covariance structure may vary from group to group. Oftentimes, the underlying population covariance matrices are not identical, yet they still have a common basic structure, e.g. there exists some rotation that diagonalizes simultaneously all covariance matrices in the groups, or all covariances can be made congruent by some translation and/or dilation. The purpose of this paper is to show how a test of homoscedasticity can be made more informative by performing a separate check for equality between shapes and equality between orientations of the concentration ellipsoids. This approach, combined with parsimonious parametrization in mixture data modeling, provides a formal hypothesis testing procedure for model assessment

Greselin, F., Ingrassia, S., & Punzo, A. (2009). Multivariate tests for patterned covariance matrices. In S. Ingrassia, & R. Rocci (a cura di), Book of Short Papers of Cladag 2009 (pp. 529-532). Padova : CLEUP.

Multivariate tests for patterned covariance matrices

Greselin, F;
2009

Abstract

In many real datasets, the same variables are measured on objects from different groups, and the covariance structure may vary from group to group. Oftentimes, the underlying population covariance matrices are not identical, yet they still have a common basic structure, e.g. there exists some rotation that diagonalizes simultaneously all covariance matrices in the groups, or all covariances can be made congruent by some translation and/or dilation. The purpose of this paper is to show how a test of homoscedasticity can be made more informative by performing a separate check for equality between shapes and equality between orientations of the concentration ellipsoids. This approach, combined with parsimonious parametrization in mixture data modeling, provides a formal hypothesis testing procedure for model assessment
No
Scientifica
Capitolo o saggio
Homoscedasticity, Spectral decomposition,Principal component analysis, F-G algorithm, Multiple tests, UI tests, IU tests.
English
Book of Short Papers of Cladag 2009
978-88-6129-406-6
Greselin, F., Ingrassia, S., & Punzo, A. (2009). Multivariate tests for patterned covariance matrices. In S. Ingrassia, & R. Rocci (a cura di), Book of Short Papers of Cladag 2009 (pp. 529-532). Padova : CLEUP.
Greselin, F; Ingrassia, S; Punzo, A
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/192196
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