Properties of the singular, inverse and generalized inverse partitioned Wishart distributions
Properties of the singular, inverse and generalized inverse partitioned Wishart distributions
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DOI：
10.1016/j.jmva.2008.02.024
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发表时间：
2008-11-01
影响因子：
1.6
通讯作者：
Okhrin, Yarema
中科院分区：
文献类型：
--
作者：
Bodnar, Taras;Okhrin, Yarema
本文讨论了Wishart分布的几种推广的分布及其独立性。首先，在奇异和逆Wishart分布的任意划分的情况下，建立了与Muirhead [R. J. Muirhead，Aspects of Multivariate Statistical Theory，Wiley，纽约，1982]的定理3.2.10类似的关于划分矩阵A =（A（ij））（i，j）= 1，2的定理。其次，在奇异分布、非中心奇异分布、逆分布和广义逆Wishart分布的情况下，得到了A（21）A（11）（-1）的密度。从投资组合理论的一个例子说明了衍生结果的重要性。(C)2008年爱思唯尔公司All rights reserved.
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(ij))(i,j) = 1,2 is established in the case of arbitrary partitioning for singular and inverse Wishart distributions. Second, the density of A(21) A(11)(-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. (C) 2008 Elsevier Inc. All rights reserved.