Geodesic
Parameter estimation of sub-Gaussian stable distributions
Kybernetika, Tome 50 (2014) no. 6, pp. 929-949.

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In this paper, we present a parameter estimation method for sub-Gaussian stable distributions. Our algorithm has two phases: in the first phase, we calculate the average values of harmonic functions of observations and in the second phase, we conduct the main procedure of asymptotic maximum likelihood where those average values are used as inputs. This implies that the main procedure of our method does not depend on the sample size of observations. The main idea of our method lies in representing the partial derivative of the density function with respect to the parameter that we estimate as the sum of harmonic functions and using this representation for finding this parameter. For fifteen summands we get acceptable precision. We demonstrate this methodology on estimating the tail index and the dispersion matrix of sub-Gaussian distributions.
DOI : 10.14736/kyb-2014-6-0929
Classification : 62A10, 62E10, 62F10, 93E10, 93E12
Keywords: stable distribution; sub-Gaussian distribution; maximum likelihood; characteristic function 
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     title = {Parameter estimation of {sub-Gaussian} stable distributions},
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     volume = {50},
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     zbl = {1307.93406},
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Omelchenko, Vadym. Parameter estimation of sub-Gaussian stable distributions. Kybernetika, Tome 50 (2014) no. 6, pp. 929-949. doi : 10.14736/kyb-2014-6-0929. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-6-0929/

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