wishart.max.par {RMTstat}R Documentation

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 n.df degrees of freedom, p.dim dimensions, population variance var, and order parameter beta.

Usage

  wishart.max.par(n.df, p.dim, var=1, beta=1)

Arguments

n.df the number of degrees of freedom for the Wishart matrix.
p.dim 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

center gives the centering.
scale gives the scaling.

Author(s)

Patrick O. Perry

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


[Package RMTstat version 0.1 Index]