Properties of the singular, inverse and generalized inverse partitioned Wishart distributions

By Taras Bodnar, Yarema Okhrin. 2008

70 citations recorded by the source corpus.

In this paper we discuss the distributions and independency properties of several generalizations of the Wishart distribution. First, an analog to Muirhead [R.J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, New York, 1982] Theorem 3.2.10 for the partitioned matrix A=(A"i"j)"i","j"="1","2 is established in the case of arbitrary partitioning for singular and inverse Wishart distributions. Second, the density of A"2"1A"1"1^-^1 is derived in the case of singular, non-central singular, inverse and generalized inverse Wishart distributions. The importance of the derived results is illustrated with an example from portfolio theory.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3e64485a346616ce223495ead9a9cdf23722f63e

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Citations in the corpus

• On the mean and variance of the generalized inverse of a singular Wishart matrix (2011, result): “Under the Lebesgue measure on the functionally independent elements, the density was proposed by Bodnar and Okhrin [2] and Zhang [18] but their results seem inconsistent.”