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

We propose estimating the scale parameter (mean of eigenvalues) scatter matrix an unspecified elliptically symmetric distribution using weights obtained by solving Tyler's M-estimator matrix. The proposed weights-based estimate (TWE) is then used to construct affine equivariant as a weighted sample covariance normalized weights. develop unified framework for unknown tail elliptical (such degrees freedom (d.o.f.) $\nu$ multivariate notation="LaTeX">$t$ (MVT) distribution). Using TWE scale, new robust d.o.f. MVT with excellent performance in heavy-tailed scenarios, outperforming other competing methods. R-package available that implements method.