Spiked Wishart Eigenvalue Centering and Scaling
Centering and scaling for the sample eigenvalue from a spiked
Wishart matrix (sample covariance matrix) with ndf degrees of
freedom, pdim dimensions, and population covariance matrix
diag(spike+var,var,var,...,var).
WishartSpikePar( spike, ndf=NA, pdim=NA, var=1, beta=1 )
spike |
the value of the spike. |
ndf |
the number of degrees of freedom for the Wishart matrix. |
pdim |
the number of dimensions (variables) for the Wishart matrix. |
var |
the population (noise) variance. |
beta |
the order parameter (1 or 2). |
The returned values give appropriate centering and scaling for the largest eigenvalue from a spiked Wishart matrix so that the centered and scaled quantity converges in distribution to a normal random variable with mean 0 and variance 1.
For the spiked distribution to exist, spike must be greater than
sqrt(pdim/ndf)*var.
Supported values for beta are 1 for real data and
and 2 for complex data.
centering |
gives the centering. |
scaleing |
gives the scaling. |
Iain M. Johnstone, Zongming Ma, Patrick O. Perry and Morteza Shahram
Baik, J., Ben Arous, G., and Péché, S. (2005). Phase transition of the largest eigenvalue for non-null complex sample covariance matrices. Annals of Probability 33, 1643–1697.
Baik, J. and Silverstein, J. W. (2006). Eigenvalues of large sample covariance matrices of spiked population models. Journal of Multivariate Analysis 97, 1382-1408.
Paul, D. (2007). Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statistica Sinica 17, 1617–1642.
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