R: White Wishart Maximum Eigenvalue Centering and Scaling

WishartMaxPar {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 `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

[Package RMTstat version 0.3 Index]