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Expansion of the Scale Mixture of the Multivariate Normal Distribution with Error Bound Evaluated in the L1-Norm

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  • Shimizu, R.

Abstract

Let Z be a random vector following the p-variate normal distribution N(0, Ip), and let S be a positive definite random matrix independent of Z. The probability density function f(x) of the random vector X = S1/2Z is expanded around that of N(0, Ip) and its error bound is evaluated in terms of the L1-norm. The bound is given in the form Ck,pE tr(S - I)k, where Ck,p is a constant depending only on k, the number of terms of the expansion, and p.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:1:p:126-138
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    Cited by:

    1. 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.

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