sEparaTe {sEparaTe}

MLE and LRT functions for separable variance-covariance structures

Description

A package for maximum likelihood estimation (MLE) of the parameters of matrix and 3rd-order tensor normal distributions with unstructured factor variance-covariance matrices (two procedures), and for unbiased modified likelihood ratio testing (LRT) of simple and double separability for variance-covariance structures (two procedures).

Functions

mle2d_svc, for maximum likelihood estimation of the parameters of a matrix normal distribution

mle3d_svc, for maximum likelihood estimation of the parameters of a 3rd-order tensor normal distribution

lrt2d_svc, for the unbiased modified likelihood ratio test of simple separability for a variance-covariance structure

lrt3d_svc, for the unbiased modified likelihood ratio test of double separability for a variance-covariance structure

Data

data2d, a two-dimensional data set

data3d, a three-dimensional data set

References

Dutilleul P. 1999. The mle algorithm for the matrix normal distribution. Journal of Statistical Computation and Simulation 64: 105-123.

Manceur AM, 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: 37-49.

Manceur AM, Dutilleul P. 2013. Unbiased modified likelihood ratio tests for simple and double separability of a variance covariance structure. Statistics and Probability Letters 83: 631-636.