Wishart and pseudo-Wishart distributions and some applications to shape theory
Journal of Multivariate Analysis
A well-conditioned estimator for large-dimensional covariance matrices
Journal of Multivariate Analysis
The Matsumoto--Yor property and the structure of the Wishart distribution
Journal of Multivariate Analysis
On improved estimation of normal precision matrix and discriminant coefficients
Journal of Multivariate Analysis
The Distribution of the Sample Minimum-Variance Frontier
Management Science
Surveillance of the covariance matrix based on the properties of the singular Wishart distribution
Computational Statistics & Data Analysis
Shrinkage algorithms for MMSE covariance estimation
IEEE Transactions on Signal Processing
On the exact and approximate distributions of the product of a Wishart matrix with a normal vector
Journal of Multivariate Analysis
An exact test about the covariance matrix
Journal of Multivariate Analysis
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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.