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New properties for Tyler’s covariance matrix estimator

Abstract : In this paper, we deal with covariance matrix estimation in complex elliptically symmetric (CES) distributions. We focus on Tyler's estimator (TyE) and the well-known sample covariance matrix (SCM). TyE is widely used in practice, but its statistical behavior is still poorly understood. On the other hand, under Gaussian assumption, the SCM is Wishart-distributed, but its properties degrade in non-Gaussian environments. The main contribution is the derivation of new properties of TyE under CES framework, in order to approximate its behavior with a simpler one, the Wishart one. Finally, Monte-Carlo simulations support that claims and demonstrate the interest of this result.
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Gordana Draskovic, Frédéric Pascal. New properties for Tyler’s covariance matrix estimator. 50th Asilomar Conference on Signals, Systems and Computers, Nov 2016, Pacific Grove, CA, United States. ⟨10.1109/acssc.2016.7869161⟩. ⟨hal-01634293⟩

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