WishartMaxPar: White Wishart Maximum Eigenvalue Centering and Scaling

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

White Wishart Maximum Eigenvalue Centering and Scaling

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

  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 April 13, 2022, 1:07 a.m.