make_sparse_model: Generate sparse linear model and random samples

In natural: Estimating the Error Variance in a High-Dimensional Linear Model

Description

Generate design matrix and response following linear models y = X β + ε, where ε ~ N(0, σ^2), and X ~ N(0, Σ).

Usage

make_sparse_model(n, p, alpha, rho, snr, nsim)

Arguments

n	the sample size
p	the number of features
alpha	sparsity, i.e., n^α nonzeros in the true regression coefficient.
rho	pairwise correlation among features
snr	signal to noise ratio, defined as β^T Σ β / σ^2
nsim	the number of simulations

Value

A list object containing:

x:

The n by p design matrix

y:

The n by nsim matrix of response vector, each column representing one replication of the simulation

beta:

The true regression coefficient vector

sigma:

The true error standard deviation

natural documentation built on May 2, 2019, 1:05 p.m.