Calculate multiway Stein's loss from component covariance matrices.
Given a list of estimated component covariance matrices, a list of true
component covariance matrices, an estimate of the total variation, and the
true total variation,
multi_stein_loss_cov will calculate multiway
Stein's loss between the estimates and the truth.
A list of positive definite matrices. These are the 'estimates' of the component covariance matrices.
A list of positive definite matrices. These are the 'true' 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.
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).
multi_stien_loss also calculates multiway Stein's loss,
but uses the lower-triangular Cholesky square roots of the component
covariance matrices as input.
A numeric, the multiway Stein's loss between the 'truth' and the 'estimates'.
Gerard, D., & Hoff, P. (2015). Equivariant minimax dominators of the MLE in the array normal model. Journal of Multivariate Analysis, 137, 32-49.