A review of Tyler's shape matrix and its extensions - UTU Tutkimustietojärjestelmä

A3 Vertaisarvioitu kirjan tai muun kokoomateoksen osa

A review of Tyler's shape matrix and its extensions

Tekijät: Taskinen, Sara; Frahm, Gabriel; Nordhausen, Klaus; Oja, Hannu

Toimittaja: Yi, Mengxi; Nordhausen, Klaus

Painos: 1

Kustantaja: Springer International Publishing

Julkaisuvuosi: 2023

Kokoomateoksen nimi: Robust and Multivariate Statistical Methods. Festschrift in Honor of David E. Tyler

Tietokannassa oleva lehden nimi: Robust and Multivariate Statistical Methods: Festschrift in Honor of David E. Tyler

Aloitussivu: 23

Lopetussivu: 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

Verkko-osoite: https://link.springer.com/chapter/10.1007/978-3-031-22687-8_2

Tiivistelmä

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.