A note on maximum likelihood estimation for covariance reducing models
Cook 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.
Volume (Year): 82 (2012)
Issue (Month): 9 ()
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- Cook, R. Dennis & Forzani, Liliana M. & Tomassi, Diego R., 2011. "LDR: A Package for Likelihood-Based Sufficient Dimension Reduction," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i03), pages -.
- 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.
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