MLE of some matrix distributions {MLE}

MLE of some matrix distributions

Description

MLE of some matrix distributions some matrix distributions.

Usage

matrix.mle(X, distr = "MN")

Arguments

X

For the matrix normal, a list with k elements (k is the sample size), k matrices of dimension n \times p each. For the matrix Fisher an array containing rotation matrices in SO(3).

distr

The distribution to fit. "MN" stands for the matrix normal, while "mfisher" stands for the matrix Fisher distribution (defined in SO(3)).

Value

For the matrix normal 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.

For the matrix Fisher the components of svd( \bar{X} ) .

Author(s)

Michail Tsagris.

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

References

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

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

Prentice M. J. (1986). Orientation statistics without parametric assumptions. Journal of the Royal Statistical Society. Series B (Methodological), 48(2): 214–222.

See Also

mv.mle, hspher.mle

Examples

## silly example
n <- 8  ;  p <- 4
X <- list()
for ( i in 1:200 )
X[[ i ]] <- matrix( rnorm(n * p), ncol = p )
mod <- matrix.mle(X)