The study of similarity between k covariance matrices Σh, referred to as k groups, under the assumption of multivariate normality is extended. Our analysis is based on the reparameterization Σh = λhΓh∆hΓ′h where λh, ∆h, and Γh specify volume, shape, and orientation of the density con- tours in each group, respectively. By allowing each of these quantities to be equal or variable between groups, one obtains eight configurations – in which homoscedasticity and heteroscedasticity represent the limit cases – characterized by a different degree of similarity. Due to its desir- able properties in the multiple testing framework, we introduce an easily implementable closed testing procedure allowing for a choice between the eight configurations. Likelihood-ratio tests are used as local tests in the procedure for their optimality properties. The proposed approach discloses a richer information on the data underlying structure than the classical existing methods, the most common one being only based on homo/heteroscedasticity. At the same time, it allows a more parsimonious parameterization, whenever the constrained model is appropriate to describe the real data. The new inferential methodology is finally applied to some well-known data sets, chosen in the multivariate literature, in order to exemplify its use. Our proposal has been also compared with some well-known likelihood-based information criteria

Greselin, F., Punzo, A. (2011). Closed likelihood-ratio testing procedures to assess similarity of covariance matrices. In A.C. Stan Azen (a cura di), Book of Abstract 5th CSDA International Conference on Computational and Financial Econometrics (CFE 2011) and 4th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics) Working Group on Computing & Statistics (ERCIM 2011) (pp. 113-113). London : ERCIM 2011.

Closed likelihood-ratio testing procedures to assess similarity of covariance matrices

Greselin, F;
2011

Abstract

The study of similarity between k covariance matrices Σh, referred to as k groups, under the assumption of multivariate normality is extended. Our analysis is based on the reparameterization Σh = λhΓh∆hΓ′h where λh, ∆h, and Γh specify volume, shape, and orientation of the density con- tours in each group, respectively. By allowing each of these quantities to be equal or variable between groups, one obtains eight configurations – in which homoscedasticity and heteroscedasticity represent the limit cases – characterized by a different degree of similarity. Due to its desir- able properties in the multiple testing framework, we introduce an easily implementable closed testing procedure allowing for a choice between the eight configurations. Likelihood-ratio tests are used as local tests in the procedure for their optimality properties. The proposed approach discloses a richer information on the data underlying structure than the classical existing methods, the most common one being only based on homo/heteroscedasticity. At the same time, it allows a more parsimonious parameterization, whenever the constrained model is appropriate to describe the real data. The new inferential methodology is finally applied to some well-known data sets, chosen in the multivariate literature, in order to exemplify its use. Our proposal has been also compared with some well-known likelihood-based information criteria
Capitolo o saggio
LIkelihood-ratio test; closed testing procedure; multipler testing procedures; patterned covariance matrice; homoscedasticity ; heteroscedasticity
English
Book of Abstract 5th CSDA International Conference on Computational and Financial Econometrics (CFE 2011) and 4th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics) Working Group on Computing & Statistics (ERCIM 2011)
Stan Azen, Ana Colubi, Erricos J. Kontoghiorghes, George Loizou and Irini Moustaki.
2011
ERCIM 2011
113
113
E951
Greselin, F., Punzo, A. (2011). Closed likelihood-ratio testing procedures to assess similarity of covariance matrices. In A.C. Stan Azen (a cura di), Book of Abstract 5th CSDA International Conference on Computational and Financial Econometrics (CFE 2011) and 4th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics) Working Group on Computing & Statistics (ERCIM 2011) (pp. 113-113). London : ERCIM 2011.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/33579
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