kroncov {TRES} | R Documentation |
The covariance estimation of tensor normal distribution
Description
This function provides the MLE of the covariance matrix of tensor normal distribution, where the covariance has a separable Kronecker structure, i.e. . The algorithm is a generalization of the MLE algorithm in Manceur, A. M., & Dutilleul, P. (2013).
Usage
kroncov(Tn, tol = 1e-06, maxiter = 10)
Arguments
Tn |
A |
tol |
The convergence tolerance with default value |
maxiter |
The maximal number of iterations. The default value is 10. |
Details
The individual component covariance matrices are not identifiable. To overcome the identifiability issue, each matrix
is normalized at the end of the iteration such that
. And an overall normalizing constant
is extracted so that the overall covariance matrix
is defined as
If Tn
is a design matrix for a multivariate random variable, then
lambda = 1
and S
is a length-one list containing the sample covariance matrix.
Value
lambda |
The normalizing constant. |
S |
A matrix list, consisting of each normalized covariance matrix |
References
Manceur, A.M. and Dutilleul, P., 2013. Maximum likelihood estimation for the tensor normal distribution: Algorithm, minimum sample size, and empirical bias and dispersion. Journal of Computational and Applied Mathematics, 239, pp.37-49.