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A Unified Approach to the Approximation of Multivariate Densities

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  • Tõnu Kollo
  • Dietrich Von Rosen

Abstract

Approximation of a density by another density is considered in the case of different dimensionalities of the distributions. The results have been derived by inverting expansions of characteristic functions with the help of matrix techniques. The approximations obtained are all functions of cumulant differences and derivatives of the approximating density. The multivariate Edgeworth expansion follows from the results as a special case. Furthermore, the density functions of the trace and eigenvalues of the sample covariance matrix are approximated by the multivariate normal density and a numerical example is given

Suggested Citation

  • Tõnu Kollo & Dietrich Von Rosen, 1998. "A Unified Approach to the Approximation of Multivariate Densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 93-109, March.
    • Handle: RePEc:bla:scjsta:v:25:y:1998:i:1:p:93-109
    DOI: 10.1111/1467-9469.t01-1-00091
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    Cited by:

    1. Withers, Christopher S. & Nadarajah, Saralees, 2014. "The dual multivariate Charlier and Edgeworth expansions," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 76-85.
    2. Loperfido, Nicola, 2024. "The skewness of mean–variance normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    3. Yong Bao & Aman Ullah, 2021. "Analytical Finite Sample Econometrics: From A. L. Nagar to Now," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 17-37, December.
    4. Kollo, Tõnu & Ruul, Kaire, 2003. "Approximations to the distribution of the sample correlation matrix," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 318-334, May.
    5. Gubhinder Kundhi & Paul Rilstone, 2020. "Simplified Matrix Methods for Multivariate Edgeworth Expansions," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(2), pages 293-326, June.

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