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Performance comparison between estimation methods of elliptical multivariate regular variation
Journal of the Korean Data & Information Science Society 2024;35:15-22
Published online January 31, 2024;
© 2024 Korean Data and Information Science Society.

Moosup Kim1

1Department of Statistics, Keimyung University
Correspondence to: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.NRF-2021R1F1A1048985).
1 Assistant professor, Department of Statistics, Keimyung University, Daegu 42601, Korea. E-mail:
Received December 27, 2023; Revised January 11, 2024; Accepted January 12, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Multivariate regular variation is characterized by tail index and spectral measure. Elliptical distributions constitute a prominent subclass, where the tail index not only is related to the magnitude of extremes but also plays the role of shape parameter for the spectral measure. Therefore, estimating the shape parameter separately can be considered for doing the spectral measure. This paper formulates the two-stage estimation procedure and conducts a comparison study. As a result, maximum likelihood estimation and the two-stage one with the Hill estimator turned out to perform better than the others.
Keywords : Elliptical distribution, maximum likelihood estimation, multivariate regular variation, performance comparison, tail index estimation, two-stage estimation.