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Inference for vast dimensional elliptical distributions

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  • Yves Dominicy
  • Hiroaki Ogata
  • David Veredas

Abstract

We propose a quantile–based method to estimate the parameters of an elliptical distribution, and a battery of tests for model adequacy. The method is suitable for vast dimensions as the estimators for location and dispersion have closed–form expressions, while estimation of the tail index boils down to univariate optimizations. The tests for model adequacy are for the null hypothesis of correct specification of one or several level contours. A Monte Carlo study to three distributions (Gaussian, Student–t and elliptical stable) for dimensions 20, 200 and 2000 reveals the goodness of the method, both in terms of computational time and finite samples. An empirical application to financial data illustrates the method. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Yves Dominicy & Hiroaki Ogata & David Veredas, 2013. "Inference for vast dimensional elliptical distributions," Computational Statistics, Springer, vol. 28(4), pages 1853-1880, August.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:4:p:1853-1880
    DOI: 10.1007/s00180-012-0384-3
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    Cited by:

    1. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    2. Michele Leonardo Bianchi & Gian Luca Tassinari & Frank J. Fabozzi, 2016. "Riding With The Four Horsemen And The Multivariate Normal Tempered Stable Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-28, June.
    3. Lorenzo Ricci & David Veredas, 2012. "TailCoR," Working Papers 1227, Banco de España.
      • Sla{dj}ana Babi'c & Christophe Ley & Lorenzo Ricci & David Veredas, 2020. "TailCoR," Papers 2011.14817, arXiv.org.
    4. Matias Heikkilä & Yves Dominicy & Pauliina Ilmonen, 2017. "Multivariate moment based extreme value index estimators," Computational Statistics, Springer, vol. 32(4), pages 1481-1513, December.
    5. Paola Stolfi & Mauro Bernardi & Lea Petrella, 2016. "Multivariate Method Of Simulated Quantiles," Departmental Working Papers of Economics - University 'Roma Tre' 0212, Department of Economics - University Roma Tre.
    6. Michele Leonardo Bianchi & Gian Luca Tassinari, 2018. "Forward-looking portfolio selection with multivariate non-Gaussian models and the Esscher transform," Papers 1805.05584, arXiv.org, revised May 2018.
    7. Christophe Ley & Anouk Neven, 2013. "Simple Le Cam Optimal Inference for the Tail Weight of Multivariate Student t Distributions: Testing Procedures and Estimation," Working Papers ECARES ECARES 2013-26, ULB -- Universite Libre de Bruxelles.

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