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Robust Likelihood Methods Based on the Skew-"t" and Related Distributions

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  • Adelchi Azzalini
  • Marc G. Genton
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    Abstract

    The robustness problem is tackled by adopting a parametric class of distributions flexible enough to match the behaviour of the observed data. In a variety of practical cases, one reasonable option is to consider distributions which include parameters to regulate their skewness and kurtosis. As a specific representative of this approach, the skew-"t" distribution is explored in more detail and reasons are given to adopt this option as a sensible general-purpose compromise between robustness and simplicity, both of treatment and of interpretation of the outcome. Some theoretical arguments, outcomes of a few simulation experiments and various wide-ranging examples with real data are provided in support of the claim. Copyright 2007 The Authors. Journal compilation (c) 2007 International Statistical Institute.

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    Bibliographic Info

    Article provided by International Statistical Institute in its journal International Statistical Review.

    Volume (Year): 76 (2008)
    Issue (Month): 1 (04)
    Pages: 106-129

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    Handle: RePEc:bla:istatr:v:76:y:2008:i:1:p:106-129

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    Cited by:
    1. Arellano-Valle, Reinaldo B. & Genton, Marc G. & Loschi, Rosangela H., 2009. "Shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 91-101, January.
    2. Ley, Christophe & Paindaveine, Davy, 2010. "On the singularity of multivariate skew-symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1434-1444, July.
    3. Ivan Pitt, 2010. "Superstar effects on royalty income in a performing rights organization," Journal of Cultural Economics, Springer, vol. 34(3), pages 219-236, August.
    4. Adcock, C.J., 2014. "Mean–variance–skewness efficient surfaces, Stein’s lemma and the multivariate extended skew-Student distribution," European Journal of Operational Research, Elsevier, vol. 234(2), pages 392-401.
    5. Luca Greco, 2011. "Minimum Hellinger distance based inference for scalar skew-normal and skew-t distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 20(1), pages 120-137, May.
    6. Teimouri, Mahdi & Nadarajah, Saralees, 2013. "On simulating Balakrishnan skew-normal variates," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 52-58.
    7. Reinaldo B. Arellano-Valle & Marc G. Genton, 2010. "Multivariate extended skew-t distributions and related families," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 201-234.
    8. Kim, Hyoung-Moon & Genton, Marc G., 2011. "Characteristic functions of scale mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1105-1117, August.
    9. Kim, Hyoung-Moon & Ryu, Duchwan & Mallick, Bani K. & Genton, Marc G., 2014. "Mixtures of skewed Kalman filters," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 228-251.
    10. Lin, Tsung I. & Ho, Hsiu J. & Chen, Chiang L., 2009. "Analysis of multivariate skew normal models with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2337-2351, November.
    11. Fung, Thomas & Seneta, Eugene, 2014. "Convergence rate to a lower tail dependence coefficient of a skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 62-72.
    12. Genton, Mark G. & Ruiz-Gazen, Anne, 2009. "Visualizing Influential Observations in Dependent Data," TSE Working Papers 09-051, Toulouse School of Economics (TSE).
    13. J. Rosco & M. Jones & Arthur Pewsey, 2011. "Skew t distributions via the sinh-arcsinh transformation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 20(3), pages 630-652, November.
    14. Olcay Arslan, 2010. "An alternative multivariate skew Laplace distribution: properties and estimation," Statistical Papers, Springer, vol. 51(4), pages 865-887, December.
    15. Adelchi Azzalini & Marc G. Genton & Bruno Scarpa, 2010. "Invariance-based estimating equations for skew-symmetric distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 275-298.
    16. Christophe Ley & Davy Paindaveine, 2010. "On Fisher information matrices and profile log-likelihood functions in generalized skew-elliptical models," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 235-250.
    17. Cancho, Vicente G. & Dey, Dipak K. & Lachos, Victor H. & Andrade, Marinho G., 2011. "Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 588-602, January.
    18. Reinaldo B. Arellano-Valle, 2010. "On the information matrix of the multivariate skew-t model," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 371-386.
    19. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2008. "The centred parametrization for the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1362-1382, August.

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