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A generalized Isserlis theorem for location mixtures of Gaussian random vectors

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  • Vignat, C.

Abstract

In a recent paper (Michalowicz et al., 2011), Michalowicz et al. provide an extension of the Isserlis theorem to the case of a Rademacher location mixture of a Gaussian vector. This theorem is known to physicists under the name of Wick’s theorem. We generalize here this result to the case of any location mixture of Gaussian vector; we also provide an example of the extension of the Isserlis theorem to a “scale–location” mixture of Gaussian, namely, the d-dimensional generalized hyperbolic distribution.

Suggested Citation

  • Vignat, C., 2012. "A generalized Isserlis theorem for location mixtures of Gaussian random vectors," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 67-71.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:1:p:67-71
    DOI: 10.1016/j.spl.2011.09.008
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    References listed on IDEAS

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    1. Vignat, C. & Bhatnagar, S., 2008. "An extension of Wick's theorem," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2404-2407, October.
    2. Kan, Raymond, 2008. "From moments of sum to moments of product," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 542-554, March.
    3. Michalowicz, J.V. & Nichols, J.M. & Bucholtz, F. & Olson, C.C., 2011. "A general Isserlis theorem for mixed-Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1233-1240, August.
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    Cited by:

    1. Yong Li & Sushanta K. Mallick & Nianling Wang & Jun Yu & Tao Zeng, 2024. "Deviance Information Criterion for Model Selection:Theoretical Justification and Applications," Working Papers 202415, University of Macau, Faculty of Business Administration.
    2. Telschow, Fabian J.E. & Davenport, Samuel & Schwartzman, Armin, 2022. "Functional delta residuals and applications to simultaneous confidence bands of moment based statistics," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    3. Li, Yong & Yu, Jun & Zeng, Tao, 2020. "Deviance information criterion for latent variable models and misspecified models," Journal of Econometrics, Elsevier, vol. 216(2), pages 450-493.
    4. Li, Yong & Yu, Jun & Zeng, Tao, 2018. "Integrated Deviance Information Criterion for Latent Variable Models," Economics and Statistics Working Papers 6-2018, Singapore Management University, School of Economics.

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