WishartSpikePar: Spiked Wishart Eigenvalue Centering and Scaling

In RMTstat: Distributions, Statistics and Tests Derived from Random Matrix Theory

Spiked Wishart Eigenvalue Centering and Scaling

Description

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).

Usage

  WishartSpikePar( spike, ndf=NA, pdim=NA, var=1, beta=1 )

Arguments

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).

Details

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.

Value

centering	gives the centering.
scaleing	gives the scaling.

Author(s)

Iain M. Johnstone, Zongming Ma, Patrick O. Perry and Morteza Shahram

References

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.

See Also

WishartSpike

RMTstat documentation built on April 13, 2022, 1:07 a.m.