New Algorithms for $M$-Estimation of Multivariate Scatter and Location

Abstract

We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms. The main idea is to utilize a second order Taylor expansion of the target functional and to devise a partial Newton-Raphson procedure. In connection with symmetrized $M$-estimators we work with incomplete $U$-statistics to accelerate our procedures initially.

References in corpus (2)

• A cautionary note on robust covariance plug-in methods
• M-Functionals of Multivariate Scatter

Cited by in corpus (8)

• Robust Sparse Covariance Estimation by Thresholding Tyler's M-Estimator
• M-Functionals of Multivariate Scatter
• Inference and Mixture Modeling with the Elliptical Gamma Distribution
• Non-Gaussian component analysis: testing the dimension of the signal subspace
• Approximating Symmetrized Estimators of Scatter via Balanced Incomplete U-Statistics
• Tyler's and Maronna's M-estimators: Non-Asymptotic Concentration Results
• Gini Covariance Matrix and its Affine Equivariant Version
• A method for sparse and robust independent component analysis