wishart.max.par {RMTstat} | R Documentation |
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
.
wishart.max.par(n.df, p.dim, var=1, beta=1)
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). |
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.
center |
gives the centering. |
scale |
gives the scaling. |
Patrick O. Perry
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].