The Sample Covariance Is Not Efficient for Elliptical Distributions

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.

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Year of publication:	2002
Authors:	Falk, Michael
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 80.2002, 2, p. 358-377
Publisher:	Elsevier
Keywords:	elliptical distribution spherically symmetric distribution local asymptotic normality (LAN) regular estimator efficient estimator

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005221511