Principal Components (PCs) in PCA are linearly uncorrelated by definition. However, uncorrelation does not imply independence (let aside the fact that each PC constructed at step t is necessarily part of the mechanisms that is used to construct the PC of the following steps, so in that sense they are strongly dependent).
My question is: would it be possible to fit a more flexible regression model to one or more PCs to detect patterns in another PC? In other words, would it be possible to use one or more PCs to predict another PC in some way?
