Affine Equivariant Tyler's M-Estimator Applied to Tail Parameter Learning of Elliptical Distributions

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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en

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IEEE Signal Processing Letters, Volume 30, pp. 1017-1021

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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.) ν 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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Ollila, E, Palomar, D P & Pascal, F 2023, 'Affine Equivariant Tyler's M-Estimator Applied to Tail Parameter Learning of Elliptical Distributions', IEEE Signal Processing Letters, vol. 30, pp. 1017-1021. https://doi.org/10.1109/LSP.2023.3301341