A note on maximum likelihood estimation for covariance reducing models
AbstractCook and Forzani (2008) proposed covariance reducing models as a method for modeling the differences among k covariance matrices. The model was developed via a property of a conditional distribution for the sample covariance matrices and this conditional distribution was used to obtain maximum likelihood estimators. In this work, we show that the same maximum likelihood estimators can be obtained using the unconditional distribution of the sample covariance matrices along with a condition on the population covariance matrices that holds if and only if the covariance reducing model holds. In addition, it is shown that when k=2, specialized numerical methods are not needed to compute the maximum likelihood estimators.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 82 (2012)
Issue (Month): 9 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- R. Dennis Cook & Liliana Forzani, 2008. "Covariance reducing models: An alternative to spectral modelling of covariance matrices," Biometrika, Biometrika Trust, vol. 95(4), pages 799-812.
- R. Dennis Cook & Liliana M. Forzani & Diego R. Tomassi, . "LDR: A Package for Likelihood-Based Sufficient Dimension Reduction," Journal of Statistical Software, American Statistical Association, vol. 39(i03).
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