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Computing the Moments of the Complex Gaussian: Full and Sparse Covariance Matrix

Author

Listed:
  • Claudia Fassino

    (Department of Mathematics, University of Genova, 16146 Genova, Italy
    These authors contributed equally to this work.)

  • Giovanni Pistone

    (Department de Castro Statistics, Collegio Carlo Alberto, 10122 Torino, Italy
    These authors contributed equally to this work.)

  • Maria Piera Rogantin

    (Department of Mathematics, University of Genova, 16146 Genova, Italy
    These authors contributed equally to this work.)

Abstract

Given a multivariate complex centered Gaussian vector Z = ( Z 1 , ⋯ , Z p ) with non-singular covariance matrix Σ , we derive sufficient conditions on the nullity of the complex moments and we give a closed-form expression for the non-null complex moments. We present conditions for the factorisation of the complex moments. Computational consequences of these results are discussed.

Suggested Citation

  • Claudia Fassino & Giovanni Pistone & Maria Piera Rogantin, 2019. "Computing the Moments of the Complex Gaussian: Full and Sparse Covariance Matrix," Mathematics, MDPI, vol. 7(3), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:263-:d:213947
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