Given a list of estimates of the lower-triangular Cholesky square roots of
component covariance matrices, a list of true lower-triangular Cholesky
square roots of component covariance matrices, an estimate of the total
variation, and the true total variation, multi_stein_loss will
calculate multiway Stein's loss between the estimates and the truth.
multi_stein_loss(B, Psi, b, psi)A list of lower triangular matrices. These are the 'estimates' of the lower-triangular Cholesky square roots of the component covariance matrices.
A list of lower triangular matrices. These are the 'true' lower-triangular Cholesky square roots of the component covariance matrices.
A numeric. This is an 'estimate' of the total variation parameter, the 'standard devation' version of it.
A numeric. This is the 'true' total variation parameter, the 'standard devation' version of it.
A numeric, the multiway Stein's loss between the 'truth' and the 'estimates'.
Multiway Stein's loss is a generalization of Stein's loss. More details on multiway Stein's loss and the Bayes rules under it can be found in Gerard and Hoff (2015).
The function multi_stien_loss_cov also calculates multiway Stein's
loss, but uses the component covariance matrices (not the Cholesky roots) as
input.
Gerard, D., & Hoff, P. (2015). Equivariant minimax dominators of the MLE in the array normal model. Journal of Multivariate Analysis, 137, 32-49. https://doi.org/10.1016/j.jmva.2015.01.020 http://arxiv.org/pdf/1408.0424.pdf