unbias.eigens: Unbiased estimation of leading eigenvalues
In SETPath: Spiked Eigenvalue Test for Pathway data

Description Usage Arguments Details Value Author(s) References Examples

View source: R/unbias.eigens.R

A function called by setpath(), used to attain unbiased estimates of leading eigenvalues and to estimate the leading eigenvalues under the null hypothesis.

1	unbias.eigens(L, g, w, minalpha = NULL)

`L`	A vector of length two containing a leading eigenvalue from each of the two datasets.
`g`	A vector of length two containing the gamma (p/n) values from the two datasets.
`w`	The weights to assign to the two classes when estimating common leading eigenvalues under the null hypothesis.
`minalpha`	Can be used to tweak the estimation of the leading eigenvalues under the null hypothesis. If NULL, eigenvalues are truncated below at 1 + 2*sqrt(gamma). Otherwise, eigenvalues are truncated below at 1 + sqrt(gamma) + minalpha.

Called by the setpath() function, not useful on its own.

`QLcorrection`	The correction factor to remove the bias in the difference between the two eigenvalues.
`a0`	The common eigenvalue estimated under the null hypothesis
`a`	The unbiased eigenvalue estimates from each class

Patrick Danaher

Patrick Danaher, Debashis Paul, and Pei Wang. "Covariance-based analyses of biological pathways." Biometrika (2015)

## The function is currently defined as
function (L, g, w, minalpha = NULL) 
{
    if (length(minalpha) == 0) {
        minalpha = sqrt(max(g))
    }
    a = c()
    for (k in 1:2) {
        if (L[k] < (1 + sqrt(g[k]))^2) {
            a[k] = 1 + sqrt(max(g)) + minalpha
        }
        if (L[k] >= (1 + sqrt(g[k]))^2) {
            a[k] = ((1 + L[k] - g[k]) + sqrt((1 + L[k] - g[k])^2 - 
                4 * L[k]))/2
        }
    }
    a0 = sum(a * w)
    a0 = max(c(a0, 1 + sqrt(g)))
    QLcorrection = (g[1] - g[2]) * a0/(a0 - 1)
    return(list(QLcorrection = QLcorrection, a0 = a0, a = a))
  }