Demeans array data.

Description

Rotates an array into two parts, one of which has mean zero.

Usage

1
demean_tensor(X, mode_reps)

Arguments

X

An array, one of whose modes is assumed to be samples from the array normal model.

mode_reps

The mode(s) that contain(s) the samples, or repetitions, from the array normal model.

Details

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.

Value

Y An array that has the same dimensions as X except that the mode mode_reps has dimension one smaller. This array is mean 0 array normal with the same covariance structure as X.

X_bar The sample mean of X. Under the array normal model, X and Y are statistically independent.

Author(s)

David Gerard.

References

Gerard, D., & Hoff, P. (2015). Equivariant minimax dominators of the MLE in the array normal model. Journal of Multivariate Analysis, 137, 32-49.

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