A Review of Tyler’s Shape Matrix and Its Extensions
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.
Main Authors
Format
Books
Book part
Published
2023
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202410256560Use this for linking
Parent publication ISBN
978-3-031-22686-1
Review status
Peer reviewed
DOI
https://doi.org/10.1007/978-3-031-22687-8_2
Language
English
Is part of publication
Robust and Multivariate Statistical Methods : Festschrift in Honor of David E. Tyler
Citation
- Taskinen, S., Frahm, G., Nordhausen, K., & Oja, H. (2023). A Review of Tyler’s Shape Matrix and Its Extensions. In M. Yi, & K. Nordhausen (Eds.), Robust and Multivariate Statistical Methods : Festschrift in Honor of David E. Tyler (pp. 23-41). Springer. https://doi.org/10.1007/978-3-031-22687-8_2
License
Copyright© 2023 the Authors