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On the Conditional Variance for Scale Mixtures of Normal Distributions

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  • Cambanis, Stamatis
  • Fotopoulos, Stergios B.
  • He, Lijian

Abstract

For a scale mixture of normal vector, X=A1/2G, where X, G[set membership, variant]n and A is a positive variable, independent of the normal vector G, we obtain that the conditional variance covariance, Cov(X2 | X1), is always finite a.s. for m[greater-or-equal, slanted]2, where X1[set membership, variant]n and m

Suggested Citation

  • Cambanis, Stamatis & Fotopoulos, Stergios B. & He, Lijian, 2000. "On the Conditional Variance for Scale Mixtures of Normal Distributions," Journal of Multivariate Analysis, Elsevier, vol. 74(2), pages 163-192, August.
    • Handle: RePEc:eee:jmvana:v:74:y:2000:i:2:p:163-192
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    References listed on IDEAS

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    1. Samorodnitsky, Gennady & Taqqu, Murad S., 1990. "Existence of joint moments of stable random variables," Statistics & Probability Letters, Elsevier, vol. 10(2), pages 167-172, July.
    2. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    3. Cambanis, Stamatis & Wu, Wei, 1992. "Multiple regression on stable vectors," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 243-272, May.
    4. Rosinski, J. & Samorodnitsky, G. & Taqqu, M. S., 1993. "Zero-One Laws for Multilinear Forms in Gaussian and Other Infinitely Divisible Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 61-82, July.
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    Cited by:

    1. B. Tarami & M. Pourahmadi, 2003. "Multi‐variate t Autoregressions: Innovations, Prediction Variances and Exact Likelihood Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(6), pages 739-754, November.
    2. Stergios Fotopoulos & Lijian He, 1999. "Error Bounds for Asymptotic Expansion of the Conditional Variance of the Scale Mixtures of the Multivariate Normal Distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(4), pages 731-747, December.
    3. Chen, Kim Heng & Jandhyala, Venkata K. & Fotopoulos, Stergios B., 2005. "Nonlinear Properties of Multifactor Financial Models," Review of Applied Economics, Lincoln University, Department of Financial and Business Systems, vol. 1(2), pages 1-27.
    4. Fotopoulos, Stergios B., 2017. "Symmetric Gaussian mixture distributions with GGC scales," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 185-194.
    5. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 73-85.
    6. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "A robust extension of the bivariate Birnbaum–Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 418-435.
    7. Fotopoulos, Stergios B., 2004. "Tempered distributions and their application in computing conditional moments for normal mixtures," Statistics & Probability Letters, Elsevier, vol. 67(3), pages 257-266, April.
    8. Fotopoulos, Stergios B. & Jandhyala, Venkata K., 2004. "Bessel inequalities with applications to conditional log returns under GIG scale mixtures of normal vectors," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 117-125, January.
    9. Fotopoulos, Stergios B. & Jandhyala, Venkata K. & Chen, Kim-Heng, 2007. "Non-linear properties of conditional returns under scale mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3041-3056, March.

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