Maximum likelihood estimation of the the matrix normal distribution {MN}

Maximum likelihood estimation of the the matrix normal distribution

Description

Maximum likelihood estimation of the the matrix normal distribution.

Usage

mn.mle(X)

Arguments

X

A list with k elements (k is the sample size), k matrices of dimension n \ times p each.

Value

A list including:

runtime

The runtime required for the whole fitting procedure.

iters

The number of iterations required for the estimation of the U and V matrices.

M

The estimated mean matrix of the distribution, a numerical matrix of dimensions n \times p.

U

The estimated covariance matrix associated with the rows, a numerical matrix of dimensions n \times n.

V

The estimated covariance matrix associated with the columns, a numerical matrix of dimensions p \times p.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

https://en.wikipedia.org/wiki/Matrix_normal_distribution#Definition

Pocuca N., Gallaugher M. P., Clark K. M. & McNicholas P. D. (2019). Assessing and Visualizing Matrix Variate Normality. arXiv:1910.02859.

See Also

dmn, rmn, ddplot

Examples

M <- as.matrix(iris[1:8, 1:4])
U <- cov( matrix( rnorm(100 * 8), ncol = 8 ) )
V <- cov( iris[1:50, 1:4] )
X <- rmn(200, M, U, V)
mod <- mn.mle(X)