| Autor: |
Ollila, Esa, Palomar, Daniel P., Pascal, Frederic |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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.) $\nu$ 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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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