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Tempered distributions and their application in computing conditional moments for normal mixtures

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  • Fotopoulos, Stergios B.

Abstract

We offer a unified theory, which provides necessary and sufficient conditions for almost everywhere convergence of radial smooth functions using Fourier integrals on Euclidean spaces. We apply this methodology to obtain expressions for the conditional variance of scale mixtures of multivariate normal. We present some specific examples, i.e., the multivariate t-distribution and when the scale is gamma distributed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:3:p:257-266
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    References listed on IDEAS

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    1. 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.
    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. Shimizu, R., 1995. "Expansion of the Scale Mixture of the Multivariate Normal Distribution with Error Bound Evaluated in the L1-Norm," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 126-138, April.
    4. Richards, Donald St. P., 1986. "Positive definite symmetric functions on finite dimensional spaces. I. Applications of the Radon transform," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 280-298, August.
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