An analytical EM algorithm for sub-gaussian vectors
| Autor: | Leonidas Sakalauskas, Ingrida Vaičiulytė, Audrius Kabašinskas |
|---|---|
| Přispěvatelé: | MDPI AG (Basel, Switzerland) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Multivariate statistics
maximum likelihood method Subordinator statistical modeling General Mathematics 0211 other engineering and technologies MathematicsofComputing_GENERAL Multivariate normal distribution α-stable distribution 02 engineering and technology 01 natural sciences 010104 statistics & probability Expectation–maximization algorithm Computer Science (miscellaneous) QA1-939 0101 mathematics EM algorithm Engineering (miscellaneous) Mathematics 021103 operations research Estimation theory Statistical model crypto-currency TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Likelihood-ratio test Computer Science::Programming Languages Random variable Algorithm |
| Zdroj: | Mathematics, Vol 9, Iss 945, p 945 (2021) Mathematics, Basel : MDPI, 2021, vol. 9, iss. 9, art. no. 945, p. 1-20 Mathematics Volume 9 Issue 9 |
| ISSN: | 2227-7390 |
| DOI: | 10.3390/math9090945 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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