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Some conditional expectation identities for the multivariate normal

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  • Withers, Christopher S.
  • Nadarajah, Saralees

Abstract

We give formulas for the conditional expectations of a product of multivariate Hermite polynomials with multivariate normal arguments. These results are extended to include conditional expectations of a product of linear combination of multivariate normals. A unified approach is given that covers both Hermite and modified Hermite polynomials, as well as polynomials associated with a matrix whose eigenvalues may be both positive and negative.

Suggested Citation

  • Withers, Christopher S. & Nadarajah, Saralees, 2010. "Some conditional expectation identities for the multivariate normal," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2250-2253, October.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:2250-2253
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    References listed on IDEAS

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    1. Withers, C. S., 2000. "A simple expression for the multivariate Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 165-169, April.
    2. Willink, R., 2005. "Normal moments and Hermite polynomials," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 271-275, July.
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