Rotates an array into two parts, one of which has mean zero.
An array, one of whose modes is assumed to be samples from the array normal model.
The mode(s) that contain(s) the samples, or repetitions, from the array normal model.
If one mode contains samples (or repetitions), then this function will rotate the array into two parts, a mean part and a covariance part. The 'covariance part' has mean zero and the rest of the methods in this package apply. The 'mean part' is simply the sample mean. If the data are array normal, then the 'covariance part' will also be array normal with the exact same covariance structure as the original tensor, except that there are one fewer samples.
Y An array that has the same dimensions as
except that the mode
mode_reps has dimension one
smaller. This array is mean 0 array normal with the same
covariance structure as
X_bar The sample mean of
X. Under the array normal
Y are statistically independent.
Gerard, D., & Hoff, P. (2015). Equivariant minimax dominators of the MLE in the array normal model. Journal of Multivariate Analysis, 137, 32-49.