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An invariance property of quadratic forms in random vectors with a selection distribution, with application to sample variogram and covariogram estimators

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  • Reinaldo Arellano-Valle

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  • Marc Genton

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  • Reinaldo Arellano-Valle & Marc Genton, 2010. "An invariance property of quadratic forms in random vectors with a selection distribution, with application to sample variogram and covariogram estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 363-381, April.
  • Handle: RePEc:spr:aistmt:v:62:y:2010:i:2:p:363-381
    DOI: 10.1007/s10463-008-0175-3
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    References listed on IDEAS

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    1. Gorsich, David J. & Genton, Marc G. & Strang, Gilbert, 2002. "Eigenstructures of Spatial Design Matrices," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 138-165, January.
    2. Hillier, Grant & Martellosio, Federico, 2006. "Spatial design matrices and associated quadratic forms: structure and properties," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 1-18, January.
    3. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    4. Genton, Marc G. & He, Li & Liu, Xiangwei, 2001. "Moments of skew-normal random vectors and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 319-325, February.
    5. Wang, Jiuzhou & Boyer, Joseph & Genton, Marc G., 2004. "A note on an equivalence between chi-square and generalized skew-normal distributions," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 395-398, March.
    6. Reinaldo B. Arellano-Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew-normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574.
    7. Marc Genton & Nicola Loperfido, 2005. "Generalized skew-elliptical distributions and their quadratic forms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 389-401, June.
    8. Arellano-Valle, R. B. & del Pino, G. & San Martín, E., 2002. "Definition and probabilistic properties of skew-distributions," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 111-121, June.
    9. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
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    Cited by:

    1. 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.
    2. Dutta, Subhajit & Genton, Marc G., 2014. "A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 82-93.
    3. 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.
    4. 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.

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