sLEDTestStat: Test statistic of sLED

In lingxuez/sLED: A Sparse Leading Eigenvalue Driven (sLED) Test for High-dimensional Matrices

Description

Calculate the sLED test statistic given a differential matrix D. A differential matrix is the difference between two symmetric relationship matrices. For any symmetric differential matrix D, sLED test statistic is defined as

max{ sEig(D), sEig(-D) }

where sEig() is the sparse leading eigenvalue, defined as

max_{v} t(v)*A*v

subject to ||v||_2 <= 1, ||v||_1 <= s.

Usage

sLEDTestStat(Dmat, rho = 1000, sumabs.seq = 0.2, niter = 20,
  trace = FALSE)

Arguments

Dmat	p-by-p numeric matrix, the differential matrix
rho	a large positive constant such that D+diag(rep(rho, p)) and -D+diag(rep(rho, p)) are positive definite.
sumabs.seq	a numeric vector specifing the sequence of sparsity parameters, each between 1/sqrt(p) and 1. Each sumabs*sqrt(p) is the upperbound of the L_1 norm of leading sparse eigenvector v.
niter	the number of iterations to use in the PMD algorithm (see symmPMD())
trace	whether to trace the progress of PMD algorithm (see symmPMD())

Value

A list containing the following components:

sumabs.seq	the sequence of sparsity parameters
rho	a positive constant to augment the diagonal of the differential matrix such that D + rho*I becomes positive definite.
stats	a numeric vector of test statistics when using different sparsity parameters (corresponding to sumabs.seq).
sign	a vector of signs when using different sparsity parameters (corresponding to sumabs.seq). Sign is "pos" if the test statistic is given by sEig(D), and "neg" if is given by sEig(-D), where sEig denotes the sparse leading eigenvalue.
v	the sequence of sparse leading eigenvectors, each row corresponds to one sparsity parameter given by sumabs.seq.
leverage	the leverage score for genes (defined as v^2 element-wise) using different sparsity parameters. Each row corresponds to one sparsity parameter given by sumabs.seq.

References

Zhu, Lei, Devlin and Roeder (2016), "Testing High Dimensional Covariance Matrices, with Application to Detecting Schizophrenia Risk Genes", arXiv:1606.00252.

See Also

sLED().

lingxuez/sLED documentation built on May 7, 2019, 2:55 a.m.