A3 Refereed book chapter or chapter in a compilation book
A review of Tyler's shape matrix and its extensions
Authors: Taskinen, Sara; Frahm, Gabriel; Nordhausen, Klaus; Oja, Hannu
Editors: Yi, Mengxi; Nordhausen, Klaus
Edition: 1
Publisher: Springer International Publishing
Publication year: 2023
Book title : Robust and Multivariate Statistical Methods. Festschrift in Honor of David E. Tyler
Journal name in source: Robust and Multivariate Statistical Methods: Festschrift in Honor of David E. Tyler
First page : 23
Last page: 41
ISBN: 978-3-031-22686-1
eISBN: 978-3-031-22687-8
DOI: https://doi.org/10.1007/978-3-031-22687-8_2
Web address : https://link.springer.com/chapter/10.1007/978-3-031-22687-8_2
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.
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.