WishartMaxPar: White Wishart Maximum Eigenvalue Centering and Scaling

Description Usage Arguments Details Value Author(s) References See Also

Description

Centering and scaling for the maximum eigenvalue from a white Wishart matrix (sample covariance matrix) with with ndf degrees of freedom, pdim dimensions, population variance var, and order parameter beta.

Usage

1
  WishartMaxPar(ndf, pdim, var=1, beta=1)

Arguments

ndf

the number of degrees of freedom for the Wishart matrix.

pdim

the number of dimensions (variables) for the Wishart matrix.

var

the population variance.

beta

the order parameter (1 or 2).

Details

If beta is not specified, it assumes the default value of 1. Likewise, var assumes a default of 1.

The returned values give appropriate centering and scaling for the largest eigenvalue from a white Wishart matrix so that the centered and scaled quantity converges in distribution to a Tracy-Widom random variable. We use the second-order accurate versions of the centering and scaling given in the references below.

Value

centering

gives the centering.

scaling

gives the scaling.

Author(s)

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

References

El Karoui, N. (2006). A rate of convergence result for the largest eigenvalue of complex white Wishart matrices. Annals of Probability 34, 2077–2117.

Ma, Z. (2008). Accuracy of the Tracy-Widom limit for the largest eigenvalue in white Wishart matrices. arXiv:0810.1329v1 [math.ST].

See Also

WishartMax, TracyWidom


RMTstat documentation built on May 2, 2019, 9:42 a.m.