R: Matrix t sampler

rmatrixt

R Documentation

Matrix t sampler

Description

Samples the matrix t-distribution.

Usage

rmatrixt(n, nu, M, U, V, checkSymmetry = TRUE, keep = TRUE)

Arguments

`n`	sample size, a positive integer
`nu`	degrees of freedom, a positive number
`M`	mean matrix, without constraints
`U`	columns covariance matrix, a positive semidefinite matrix of order equal to `nrow(M)`
`V`	rows covariance matrix, a positive semidefinite matrix of order equal to `ncol(M)`
`checkSymmetry`	logical, whether to check the symmetry of `U` and `V`
`keep`	logical, whether to return an array with class keep

Value

A numeric three-dimensional array; simulations are stacked along the third dimension (see example).

Note

When p=1 and V=nu or when m=1 and U=nu, the distribution is the multivariate t-distribution.

Examples

nu <- 4
m <- 2
p <- 3
M <- matrix(1, m, p)
U <- toeplitz(m:1)
V <- toeplitz(p:1)
Tsims <- rmatrixt(10000, nu, M, U, V)
dim(Tsims) # 2 3 10000
apply(Tsims, 1:2, mean) # approximates M
vecTsims <- t(apply(Tsims, 3, function(X) c(t(X))))
round(cov(vecTsims), 1) # approximates 1/(nu-2) * kronecker(U,V)
## the `keep` class is nice when m=1 or p=1:
Tsims <- rmatrixt(2, nu, M=1:3, U=diag(3), V=1)
Tsims[,,1] # dimensions 3 1
# without `keep`, dimensions are lost:
rmatrixt(2, nu, M=1:3, U=diag(3), V=1, keep=FALSE)[,,1]