Contains inferential and graphical routines for comparing two treatment arms in terms of the restricted mean time in favor of treatment.

We generate random variables following general Marchenko-Pastur distribution and Tracy-Widom distribution. We compute limits and distributions of eigenvalues and generalized components of spiked covariance matrices. We give estimation of all population eigenvalues of spiked covariance matrix model. We give tests of population covariance matrix. We also perform matrix denoising for signal-plus-noise model.

An algorithm which can be used to determine an objective threshold for signal-noise separation in large random matrices (correlation matrices, mutual information matrices, network adjacency matrices) is provided. The package makes use of the results of Random Matrix Theory (RMT). The algorithm increments a suppositional threshold monotonically, thereby recording the eigenvalue spacing distribution of the matrix. According to RMT, that distribution undergoes a characteristic change when the threshold properly separates signal from noise. By using the algorithm, the modular structure of a matrix - or of the corresponding network - can be unraveled.

Efficient solvers for 10 regularized multi-task learning algorithms applicable for regression, classification, joint feature selection, task clustering, low-rank learning, sparse learning and network incorporation. Based on the accelerated gradient descent method, the algorithms feature a state-of-art computational complexity O(1/k^2). Sparse model structure is induced by the solving the proximal operator. The detail of the package is described in the paper of Han Cao and Emanuel Schwarz (2018) <doi:10.1093/bioinformatics/bty831>.

Functions for working with the Tracy-Widom laws and other distributions 
    related to the eigenvalues of large Wishart matrices.
    The tables for computing the Tracy-Widom densities and distribution
    functions were computed by functions were computed by Momar Dieng's MATLAB package "RMLab". This package is part of a collaboration between Iain Johnstone, Zongming Ma, Patrick Perry, and Morteza Shahram.