A Review of Tyler’s Shape Matrix and Its Extensions

Sara Taskinen (), Gabriel Frahm (), Klaus Nordhausen () and Hannu Oja ()
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Sara Taskinen: University of Jyväskylä, Department of Mathematics and Statistics
Gabriel Frahm: Helmut Schmidt University, Department of Mathematics and Statistics
Klaus Nordhausen: University of Jyväskylä, Department of Mathematics and Statistics
Hannu Oja: University of Turku, Department of Mathematics and Statistics

A chapter in Robust and Multivariate Statistical Methods, 2023, pp 23-41 from Springer

Abstract: Abstract In a seminal paper, Tyler (1987a) suggests an M-estimator for shape, which is now known as Tyler’s shape matrix. Tyler’s shape matrix is increasingly popular due to its nice statistical properties. It is distribution free within the class of generalized elliptical distributions. Further, under very mild regularity conditions, it is consistent and asymptotically normally distributed after the usual standardization. Tyler’s shape matrix is still the subject of active research, e.g., in the signal processing literature, which discusses structured and regularized shape matrices. In this article, we review Tyler’s original shape matrix and some recent developments.

Keywords: M-estimator; Generalized elliptical distribution; High dimension; Robust estimator; Regularization (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/978-3-031-22687-8_2

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