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Mixture modeling for efficiently estimating the spectral distribution of bivariate regular variation
Journal of the Korean Data & Information Science Society 2021;32:679-94
Published online May 31, 2021;
© 2021 Korean Data and Information Science Society.

Moosup Kim1

1Department of Statistics, Keimyung University
Correspondence to: 1 Assistant professor, Department of Statistics, Keimyung University, Daegu 42601, Korea. Email:
Received February 22, 2021; Revised March 30, 2021; Accepted April 7, 2021.
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.
This paper considers the parametric estimation of the spectral distribution of bivariate regular variation for efficiency. Since Fisher consistency is the key condition for attaining efficiency, mixture model is employed as the parametric model class due to its flexibility. The maximum likelihood estimation is shown to be asymptotically efficient under some regularity conditions. Moreover, in the real data analysis, the maximum likelihood method based on normal mixture produces an estimation result of spectral distribution well fitted to the data.
Keywords : mixture model, bivariate regular variation, spectral distribution, efficiency