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Optimal Ridge-type Estimators of Covariance Matrix in High Dimension

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  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

  • Muni S. Srivastava

    (Department of Statistics, University of Toronto)

Abstract

　　 The problem of estimating the covariance matrix of normal and non-normal distributions is addressed when both the sample size and the dimension of covariance matrix tend to in nity. In this paper, we consider a class of ridge-type estimators which are linear combinations of the unbiased estimator and the identity matrix multiplied by a scalor statistic, and we derive a leading term of their risk functions relative to a quadratic loss function. Within this class, we obtain the optimal ridge-type estimator by minimizing the leading term in the risk approximation. It is interesting to note that the optimal weight is based on a statistic for testing sphericity of the covariance matrix.

Suggested Citation

  • Tatsuya Kubokawa & Muni S. Srivastava, 2013. "Optimal Ridge-type Estimators of Covariance Matrix in High Dimension," CIRJE F-Series CIRJE-F-906, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2013cf906
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    References listed on IDEAS

    as
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