| Title |
An analytical EM algorithm for sub-gaussian vectors |
| Authors |
Kabašinskas, Audrius ; Sakalauskas, Leonidas ; Vaičiulytė, Ingrida |
| DOI |
10.3390/math9090945 |
| Full Text |
|
| Is Part of |
Mathematics.. Basel : MDPI. 2021, vol. 9, iss. 9, art. no. 945, p. 1-20.. ISSN 2227-7390 |
| Keywords [eng] |
EM algorithm ; maximum likelihood method ; statistical modeling ; α-stable distribution ; crypto-currency |
| Abstract [eng] |
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. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2021 |
| CC license |
|
