Parameter estimation of sub-Gaussian stable distributions

Vadym Omelchenko

Kybernetika (2014)

  • Volume: 50, Issue: 6, page 929-949
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Omelchenko, Vadym. "Parameter estimation of sub-Gaussian stable distributions." Kybernetika 50.6 (2014): 929-949. <http://eudml.org/doc/262151>.

@article{Omelchenko2014,
abstract = {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.},
author = {Omelchenko, Vadym},
journal = {Kybernetika},
keywords = {stable distribution; sub-Gaussian distribution; maximum likelihood; characteristic function; stable distribution; sub-Gaussian distribution; maximum likelihood; characteristic function},
language = {eng},
number = {6},
pages = {929-949},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Parameter estimation of sub-Gaussian stable distributions},
url = {http://eudml.org/doc/262151},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Omelchenko, Vadym
TI - Parameter estimation of sub-Gaussian stable distributions
JO - Kybernetika
PY - 2014
PB - Institute of Information Theory and Automation AS CR
VL - 50
IS - 6
SP - 929
EP - 949
AB - 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.
LA - eng
KW - stable distribution; sub-Gaussian distribution; maximum likelihood; characteristic function; stable distribution; sub-Gaussian distribution; maximum likelihood; characteristic function
UR - http://eudml.org/doc/262151
ER -

References

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