mgc (version 2.0.2)

mgc.sims.joint: Joint Normal Simulation

Description

A function for Generating a joint-normal simulation.

Usage

mgc.sims.joint(n, d, eps = 0.5)

Arguments

n

the number of samples for the simulation.

d

the number of dimensions for the simulation setting.

eps

the noise level for the simulation. Defaults to 0.5.

Value

a list containing the following:

X

[n, d] the data matrix with n samples in d dimensions.

Y

[n] the response array.

Details

Given: \(\rho = \frac{1}{2}d\), \(I_d\) is the identity matrix of size \(d \times d\), \(J_d\) is the matrix of ones of size \(d \times d\). Simulates \(n\) points from \(Joint-Normal(X, Y) \in \mathbf{R}^d \times \mathbf{R}^d\), where: $$(X, Y) \sim {N}(0, \Sigma)$$, $$\Sigma = \left[I_d, \rho J_d; \rho J_d , (1 + \epsilon\kappa)I_d\right]$$ and \(\kappa = 1\textrm{ if }d = 1, \textrm{ and 0 otherwise}\) controls the noise for higher dimensions.

For more details see the help vignette: vignette("sims", package = "mgc")

Examples

# NOT RUN {
library(mgc)
result  <- mgc.sims.joint(n=100, d=10)  # simulate 100 samples in 10 dimensions
X <- result$X; Y <- result$Y
# }