A Review of Tyler’s Shape Matrix and Its Extensions

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

doi:10.1007/978-3-031-22687-8_2

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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

Tekijät

Taskinen, Sara |

Frahm, Gabriel |

Nordhausen, Klaus |

Oja, Hannu

Toimittajat

Yi, Mengxi |

Nordhausen, Klaus

Päivämäärä

2023

Tekijänoikeudet

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.

Julkaisija

Springer

Emojulkaisun ISBN

978-3-031-22686-1

Kuuluu julkaisuun

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

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