Whitening a dataset with fewer observations than variables

Question

I have a k x n dataset where k equals the number of variables and n equals the number of observations per variable. I know these data are correlated and I would like to whiten them with the ordinary whitening transformation. Inconveniently, k outnumbers n by far, so that when estimating the k x k covariance matrix it will not be invertible. To get around this problem, I estimated the covariance matrix using optimal shrinkage, but the obtained covariance matrix is not suited for whitening anymore.

I’d be grateful for ideas on how to whiten these data.

covariance matrix regularization

I'd be grateful for ideas on how to whiten these data.

kjetil b halvorsen · Answer

You didn't tell us why you want to whiten the data, but, however, you could simply use the generalized inverse of the sample covariance matrix the same way you uses its inverse (when it exists). It should have the same effect. (I can add details if wanted)

Answered by kjetil b halvorsen on December 5, 2021

Whitening a dataset with fewer observations than variables

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