Distribution and characteristic functions for correlated complex Wishart matrices
نویسندگان
چکیده
منابع مشابه
Eigenvalue density of correlated complex random Wishart matrices.
Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M dagger M where M is a complex matrix drawn from a normalized distribution P(M) approximately exp(-Tr [AMB M dagger]) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called correlated Wishart matrices occur in many fields ranging from information theo...
متن کاملExtreme Eigenvalue Distributions of Some Complex Correlated Non-Central Wishart and Gamma-Wishart Random Matrices
Let W be a correlated complex non-central Wishart matrix defined through W = XX, where X is n × m (n ≥ m) complex Gaussian with non-zero mean Υ and non-trivial covariance Σ. We derive exact expressions for the cumulative distribution functions (c.d.f.s) of the extreme eigenvalues (i.e., maximum and minimum) of W for some particular cases. These results are quite simple, involving rapidly conver...
متن کاملComplex singular Wishart matrices and applications∗
In this paper, complex singular Wishart matrices and their applications are investigated. In particular, a volume element on the space of positive semidefinite m×m complex matrices of rank n < m is introduced and some transformation properties are established. The Jacobian for the change of variables in the singular value decomposition of general m × n complex matrices is derived. Then the dens...
متن کاملLarge Complex Correlated Wishart Matrices: Fluctuations and Asymptotic Independence at the Edges
We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eigenvalue distribution may have several connected components. Under mild conditions for the population matrices, we show that for every generic positive edge of that support, there exists an extremal eigenvalue which co...
متن کاملOn moments of complex Wishart and complex inverse Wishart distributed matrices
This paper addresses the calculation of moments of complex Wishart and complex inverse Wishart distributed random matrices. Complex Wishart and complex inverse Wishart distributed random matrices are used in applications like radar, sonar, or seismics in order to model the statistical properties of complex sample covariance matrices and complex inverse sample covariance matrices, respectively. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2007
ISSN: 0047-259X
DOI: 10.1016/j.jmva.2006.09.013