White Wishart Maximum Eigenvalue Centering and Scaling
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.
WishartMaxPar(ndf, pdim, var=1, beta=1)
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). |
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.
centering |
gives the centering. |
scaling |
gives the scaling. |
Iain M. Johnstone, Zongming Ma, Patrick O. Perry and Morteza Shahram
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].
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