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 Inform. Primen., 2014, Volume 8, Issue 4, Pages 11–19 (Mi ia338)

A modified grid method for statistical separation of normal variance-mean mixtures

V. Yu. Korolevab, A. Yu. Korchaginb

a Institute of Informatics Problems, Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
b Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation

Abstract: A modified two-stage grid method for statistical separation of normal variance-mean mixtures is described as an alternative to a pure EM (expectation-maximization) algorithm. At the first stage of this algorithm, a discrete approximation is constructed to the mixing distribution. At the second stage, the obtained discrete distribution is approximated by an absolutely continuous distribution from a predetermined family, say, by a generalized inverse Gaussian distribution. The convergence of this two-stage procedure is discussed. The monotonicity of the grid procedure used at the first stage is proved. The problem of the optimal choice of the parameters of the method is discussed in detail. First of all, the problem of the optimal choice of the grid thrown on the support of the mixing distribution is considered. Statistical estimators are proposed for the quantiles of the mixing law. The efficiency of the method is illustrated by examples of its application to the estimation of the parameters of generalized hyperbolic distributions.

Keywords: mixture of probability distributions; normal variance-mean mixture; generalized hyperbolic distribution; EM-algorithm; grid method of separation of mixtures.

DOI: https://doi.org/10.14357/19922264140402

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Citation: V. Yu. Korolev, A. Yu. Korchagin, “A modified grid method for statistical separation of normal variance-mean mixtures”, Inform. Primen., 8:4 (2014), 11–19

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\Bibitem{KorKor14} \by V.~Yu.~Korolev, A.~Yu.~Korchagin \paper A modified grid method for statistical separation of normal variance-mean mixtures \jour Inform. Primen. \yr 2014 \vol 8 \issue 4 \pages 11--19 \mathnet{http://mi.mathnet.ru/ia338} \crossref{https://doi.org/10.14357/19922264140402} \elib{http://elibrary.ru/item.asp?id=22846460} 

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This publication is cited in the following articles:
1. V. Yu. Korolev, A. Yu. Korchagin, I. A. Sokolov, “Obobschennye dispersionnye gamma-raspredeleniya kak modeli statisticheskikh zakonomernostei na finansovykh rynkakh”, Inform. i ee primen., 9:4 (2015), 14–28
2. V. Yu. Korolev, A. Yu. Korchagin, A. I. Zeifman, “Teorema Puassona dlya skhemy ispytanii Bernulli so sluchainoi veroyatnostyu uspekha i diskretnyi analog raspredeleniya Veibulla”, Inform. i ee primen., 10:4 (2016), 11–20
3. V. Yu. Korolev, “Nekotorye svoistva raspredeleniya Mittag-Lefflera i svyazannykh s nim protsessov”, Inform. i ee primen., 11:4 (2017), 26–37
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