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Article

An Analytical EM Algorithm for Sub-Gaussian Vectors

1
Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 51368 Kaunas, Lithuania
2
Šiauliai Academy, Vilnius University, 76352 Šiauliai, Lithuania
3
Faculty of Business and Technologies, Šiauliai State College, 76241 Šiauliai, Lithuania
*
Author to whom correspondence should be addressed.
Academic Editor: Filipe J. Marques
Mathematics 2021, 9(9), 945; https://doi.org/10.3390/math9090945
Received: 8 April 2021 / Revised: 19 April 2021 / Accepted: 21 April 2021 / Published: 23 April 2021
The area in which a multivariate α-stable distribution could be applied is vast; however, a lack of parameter estimation methods and theoretical limitations diminish its potential. Traditionally, the maximum likelihood estimation of parameters has been considered using a representation of the multivariate stable vector through a multivariate normal vector and an α-stable subordinator. This paper introduces an analytical expectation maximization (EM) algorithm for the estimation of parameters of symmetric multivariate α-stable random variables. Our numerical results show that the convergence of the proposed algorithm is much faster than that of existing algorithms. Moreover, the likelihood ratio (goodness-of-fit) test for a multivariate α-stable distribution was implemented. Empirical examples with simulated and real world (stocks, AIS and cryptocurrencies) data showed that the likelihood ratio test can be useful for assessing goodness-of-fit. View Full-Text
Keywords: EM algorithm; maximum likelihood method; statistical modeling; α-stable distribution; crypto-currency EM algorithm; maximum likelihood method; statistical modeling; α-stable distribution; crypto-currency
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MDPI and ACS Style

Kabašinskas, A.; Sakalauskas, L.; Vaičiulytė, I. An Analytical EM Algorithm for Sub-Gaussian Vectors. Mathematics 2021, 9, 945. https://doi.org/10.3390/math9090945

AMA Style

Kabašinskas A, Sakalauskas L, Vaičiulytė I. An Analytical EM Algorithm for Sub-Gaussian Vectors. Mathematics. 2021; 9(9):945. https://doi.org/10.3390/math9090945

Chicago/Turabian Style

Kabašinskas, Audrius, Leonidas Sakalauskas, and Ingrida Vaičiulytė. 2021. "An Analytical EM Algorithm for Sub-Gaussian Vectors" Mathematics 9, no. 9: 945. https://doi.org/10.3390/math9090945

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