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The asymptotic distributions of the statistics of the skew elliptical variables

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Abstract

In this paper, the asymptotic properties of the quadratic forms and theT statistic of the skew elliptical variables are studied. Consistent estimators of some parameters are obtained. The robustness of the significance level of the one-sided t test within the family of the skew normal family is investigated.

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References

  1. Azzalini, A., Dalla Valle, A., The multivariate skew-normal distribution, Biometrika, 1996, 83: 715–726.

    Article  MATH  MathSciNet  Google Scholar 

  2. Azzalini, A., Capitanio, A., Statistical applications of the multivariate skew normal distribution, J. R. Statist. Soc. B., 1999, 61: 579–602.

    Article  MATH  MathSciNet  Google Scholar 

  3. Branco, M. D., Dey, D. K., A general class of multivariate skew-elliptical distributions, Journal of Multivariate Analysis, 2001, 79: 99–113.

    Article  MATH  MathSciNet  Google Scholar 

  4. Fang, B. Q., The skew elliptical distributions and their quadratic forms, Journal of Multivariate Analysis, 2003, 87: 298–314.

    Article  MATH  MathSciNet  Google Scholar 

  5. Fang, B. Q., Thet statistic of the skew elliptical distributions, AMSS Technical Report 2002–008, Chinese Academy of Sciences, 2002.

  6. Fang, B. Q., Non-central quadratic forms of the skew elliptical variables, AMSS Technical Report 2002–043, Chinese Academy of Sciences, 2002.

  7. Fang, K. T., Kotz, S., Ng, K. W., Symmetric Multivariate and Related Distributions, London: Chapman and Hall, 1990.

    MATH  Google Scholar 

  8. Arnold, B. C., Beaver, R. J., Hidden truncation models, Sankhyā, 2000, 62: 23–35.

    MATH  MathSciNet  Google Scholar 

  9. Johnson, N. L., Kotz, S., Balakrishnan, N., Continuous Univariate Distributions, Vol. 2, 2nd ed., New York: Wiley, 1995.

    MATH  Google Scholar 

  10. Lehmann, E. L., Testing Statistical Hypotheses, 2nd ed., New York: Wiley, 1986.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, China

    Biqi Fang

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  1. Biqi Fang
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Correspondence to Biqi Fang.

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Fang, B. The asymptotic distributions of the statistics of the skew elliptical variables. Sci. China Ser. A-Math. 48, 214–221 (2005). https://doi.org/10.1360/03ys0225

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  • DOI: https://doi.org/10.1360/03ys0225

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