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On the existence of non-central Wishart distributions

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  • Mayerhofer, Eberhard

Abstract

This paper deals with the existence issue of non-central Wishart distributions which is a research topic initiated by Wishart (1928), [10] and with important contributions by e.g., Lévy (1937) [7], Gindikin (1975) [4], Shanbhag (1988) [9], Peddada and Richards (1991) [8]. We present a new method involving the theory of affine Markov processes, which reveals joint necessary conditions on the shape and non-centrality parameter. While Eaton’s conjecture concerning the necessary range of the shape parameter is confirmed, we also observe that it is not sufficient anymore that it only belongs to the Gindikin ensemble, as is in the central case.

Suggested Citation

  • Mayerhofer, Eberhard, 2013. "On the existence of non-central Wishart distributions," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 448-456.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:448-456
    DOI: 10.1016/j.jmva.2012.07.010
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    References listed on IDEAS

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    1. Christa Cuchiero & Damir Filipovi'c & Eberhard Mayerhofer & Josef Teichmann, 2009. "Affine processes on positive semidefinite matrices," Papers 0910.0137, arXiv.org, revised Apr 2011.
    2. Letac, Gérard & Massam, Hélène, 2008. "The noncentral Wishart as an exponential family, and its moments," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1393-1417, August.
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    Cited by:

    1. Graczyk, Piotr & Małecki, Jacek & Mayerhofer, Eberhard, 2018. "A characterization of Wishart processes and Wishart distributions," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1386-1404.
    2. Letac, Gérard & Massam, Hélène, 2018. "The Laplace transform (dets)−pexptr(s−1w) and the existence of non-central Wishart distributions," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 96-110.
    3. Francesca Biagini & Alessandro Gnoatto & Maximilian Hartel, 2013. "Affine HJM Framework on $S_{d}^{+}$ and Long-Term Yield," Papers 1311.0688, arXiv.org, revised Aug 2015.

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