Calculate the sLME given a matrix \(D\).
For any symmetric matrix \(D\), sLME test statistic is defined as
$$max{ sEig(D), sEig(-D) }$$
where sEig() is the sparse leading eigenvalue, defined as
$$max_{v} v^T A v$$
subject to
\(||v||_2 \leq 1, ||v||_1 \leq s\).
sLME(Dmat, rho = 1000, sumabs.seq = 0.2, niter = 20, trace = FALSE)A list containing the following components:
the sequence of sparsity parameters
a positive constant to augment the diagonal of the differential matrix such that \(D + rho*I\) becomes positive definite.
a numeric vector of test statistics when using different sparsity parameters
(corresponding to sumabs.seq).
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.
the sequence of sparse leading eigenvectors, each row corresponds to one sparsity
parameter given by sumabs.seq.
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.
p-by-p numeric matrix, the differential matrix
a large positive constant such that \(D+diag(rep(rho, p))\) and \(-D+diag(rep(rho, p))\) are positive definite.
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 \(v\).
the number of iterations to use in the PMD algorithm (see symmPMD())
whether to trace the progress of PMD algorithm (see symmPMD())
Zhu, Lingxue, et al. "Testing high-dimensional covariance matrices, with application to detecting schizophrenia risk genes." The annals of applied statistics 11.3 (2017): 1810.