robustmatrix (version 0.1.3)

mmle: Maximum Likelihood Estimation for Matrix Normal Distribtuion

Description

mmle computes the Maximum Likelihood Estimators (MLEs) for the matrix normal distribution using the iterative flip-flop algorithm Dutilleul1999robustmatrix.

Usage

mmle(X, max_iter = 100L, lambda = 0, silent = FALSE)

Value

A list containing the following:

mu

Estimated \(p \times q\) mean matrix.

cov_row

Estimated \(p\) times \(p\) rowwise covariance matrix.

cov_col

Estimated \(q\) times \(q\) columnwise covariance matrix.

cov_row_inv

Inverse of cov_row.

cov_col_inv

Inverse of cov_col.

norm

Forbenius norm of squared differences between covariance matrices in final iteration.

iterations

Number of iterations of the mmle procedure.

Arguments

X

a 3d array of dimension \((p,q,n)\), containing \(n\) matrix-variate samples of \(p\) rows and \(q\) columns in each slice.

max_iter

upper limit of iterations.

lambda

a smooting parameter for the rowwise and columnwise covariance matrices.

silent

Logical. If FALSE (default) warnings and errors are printed.

References

See Also

For robust parameter estimation use mmcd.

Examples

n = 1000; p = 2; q = 3
mu = matrix(rep(0, p*q), nrow = p, ncol = q)
cov_row = matrix(c(1,0.5,0.5,1), nrow = p, ncol = p)
cov_col = matrix(c(3,2,1,2,3,2,1,2,3), nrow = q, ncol = q)
X <- rmatnorm(n = 1000, mu, cov_row, cov_col)
par_mmle <- mmle(X)