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A note on maximum likelihood estimation for covariance reducing models

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  • Schott, James R.
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 9 ()
    Pages: 1629-1631

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:9:p:1629-1631

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    Related research

    Keywords: Eigenanalysis; Wishart distribution;

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    1. 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, American Statistical Association, vol. 39(i03).
    2. R. Dennis Cook & Liliana Forzani, 2008. "Covariance reducing models: An alternative to spectral modelling of covariance matrices," Biometrika, Biometrika Trust, Biometrika Trust, vol. 95(4), pages 799-812.
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