The Sample Covariance Is Not Efficient for Elliptical Distributions

Michael Falk

Journal of Multivariate Analysis, 2002, vol. 80, issue 2, 358-377

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.

Keywords: elliptical; distribution; spherically; symmetric; distribution; local; asymptotic; normality; (LAN); regular; estimator; efficient; estimator (search for similar items in EconPapers)
Date: 2002
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