On the existence of non-central Wishart distributions

Eberhard Mayerhofer

Journal of Multivariate Analysis, 2013, vol. 114, issue C, 448-456

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.

Keywords: Non-central Wishart distribution; Gindikin ensemble; Wishart processes; Affine processes (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:114:y:2013:i:c:p:448-456

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DOI: 10.1016/j.jmva.2012.07.010

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