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Moments of elliptically distributed random variates

Author

Listed:
  • Berkane, Maia
  • Bentler, P. M.

Abstract

This paper presents an inductive method for computing the moments of an elliptically distributed random variate. A sequence of new parameters relating higher-order to second moments is introduced. The known kurtosis parameter is shown to be a member of this sequence.

Suggested Citation

  • Berkane, Maia & Bentler, P. M., 1986. "Moments of elliptically distributed random variates," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 333-335, October.
    • Handle: RePEc:eee:stapro:v:4:y:1986:i:6:p:333-335
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    Citations

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    Cited by:

    1. Nakagawa, Shigekazu & Niki, Naoto & Hashiguchi, Hiroki, 1998. "Computer algebra application to the distribution of sample correlation coefficient," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 45(1), pages 23-32.
    2. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & György H. Terdik, 2021. "Asymptotic theory for statistics based on cumulant vectors with applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 708-728, June.
    3. Cysneiros, Francisco Jose A. & Paula, Gilberto A., 2005. "Restricted methods in symmetrical linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 689-708, June.
    4. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2016. "Inference in VARs with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 191(1), pages 69-85.
    5. Francisco M. C. Medeiros & Silvia L. P. Ferrari, 2017. "Small-sample testing inference in symmetric and log-symmetric linear regression models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(3), pages 200-224, August.
    6. Amengual, Dante & Fiorentini, Gabriele & Sentana, Enrique, 2013. "Sequential estimation of shape parameters in multivariate dynamic models," Journal of Econometrics, Elsevier, vol. 177(2), pages 233-249.
    7. Pier Francesco Procacci & Tomaso Aste, 2021. "Portfolio Optimization with Sparse Multivariate Modelling," Papers 2103.15232, arXiv.org.
    8. Maia Berkane & P. M. Bentler, 1988. "Estimation of Contamination Parameters and Identification of Outliers in Multivariate Data," Sociological Methods & Research, , vol. 17(1), pages 55-64, August.
    9. Sreenivasa Rao Jammalamadaka & Emanuele Taufer & Gyorgy H. Terdik, 2021. "On Multivariate Skewness and Kurtosis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 607-644, August.
    10. Pier Francesco Procacci & Tomaso Aste, 2022. "Portfolio optimization with sparse multivariate modeling," Journal of Asset Management, Palgrave Macmillan, vol. 23(6), pages 445-465, October.
    11. Gabriele Fiorentini & Enrique Sentana, 2007. "On the Efficiency and Consistency of Likelihood Estimation in Multivariate Conditionally Heteroskedastic Dynamic Regression Models," Working Papers wp2007_0713, CEMFI.
    12. Song, Iickho & Lee, Seungwon, 2015. "Explicit formulae for product moments of multivariate Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 27-34.
    13. repec:rim:rimwps:38-07 is not listed on IDEAS
    14. Kan, Raymond, 2008. "From moments of sum to moments of product," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 542-554, March.
    15. Cordeiro, Gauss M. & Ferrari, Silvia L. P. & Uribe-Opazo, Miguel A. & Vasconcellos, Klaus L. P., 2000. "Corrected maximum-likelihood estimation in a class of symmetric nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 317-328, February.

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