A3 Refereed book chapter or chapter in a compilation book

A review of Tyler's shape matrix and its extensions




AuthorsTaskinen, Sara; Frahm, Gabriel; Nordhausen, Klaus; Oja, Hannu

EditorsYi, Mengxi; Nordhausen, Klaus

Edition1

PublisherSpringer International Publishing

Publication year2023

Book title Robust and Multivariate Statistical Methods. Festschrift in Honor of David E. Tyler

Journal name in sourceRobust and Multivariate Statistical Methods: Festschrift in Honor of David E. Tyler

First page 23

Last page41

ISBN978-3-031-22686-1

eISBN978-3-031-22687-8

DOIhttps://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.



Last updated on 2025-17-02 at 08:54