Journal
IEEE SIGNAL PROCESSING LETTERS
Volume 30, Issue -, Pages 1017-1021Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LSP.2023.3301341
Keywords
Covariance matrix; elliptical distributions; scatter matrix; Tyler's M-estimator
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This paper proposes a method to estimate the scale parameter of the scatter matrix using weights obtained from Tyler's M-estimator. The estimated scale parameter is used to construct an affine equivariant Tyler's M-estimator. Additionally, a unified framework for estimating the tail parameter of elliptical distributions is developed, with a new robust estimate proposed for the degrees of freedom parameter in the multivariate t distribution.
We propose estimating the scale parameter (mean of the eigenvalues) of the scatter matrix of an unspecified elliptically symmetric distribution using weights obtained by solving Tyler's M-estimator of the scatter matrix. The proposed Tyler's weights based estimate (TWE) of scale is then used to construct an affine equivariant Tyler's M-estimator as a weighted sample covariance matrix using normalized Tyler's weights. We then develop a unified framework for estimating the unknown tail parameter of the elliptical distribution (such as the degrees of freedom (d.o.f.) ? of the multivariate t (MVT) distribution). Using the proposed TWE of scale, a new robust estimate of the d.o.f. parameter of MVT distribution is proposed with excellent performance in heavy-tailed scenarios, outperforming other competing methods. R-package is available that implements the proposed method.
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