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The Sample Covariance Is Not Efficient for Elliptical Distributions

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  • Falk, Michael

Abstract

It is well known that the sample covariance is not an efficient estimator of the covariance of a bivariate normal vector. We extend this result to elliptical distributions and we propose a simple explicit estimator, which is efficient in the normal case and which outperforms the sample covariance in general. Necessary and sufficient conditions are established under which this estimator is in general efficient for an elliptical distribution.

Suggested Citation

  • Falk, Michael, 2002. "The Sample Covariance Is Not Efficient for Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 358-377, February.
    • Handle: RePEc:eee:jmvana:v:80:y:2002:i:2:p:358-377
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    References listed on IDEAS

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    1. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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