I have received a reviewer's comment on a paper which applies PCA to reduce the size of a problem and the application is in the robust optimization field. The reviewer implies that "In robust optimization, approximating the problem using PCA could be fatal because PCA creates uncontrollable distortions.". However no reference has been mentioned to address this point and my search for an answer didn't result in any reason for this comment. Would anyone please help me with a reason for this comment or introduce a book or paper that addresses this issue. Your help is greatly appreciated!
Possibly she is referring to the fact that classical PCA is not robust in the sense that its asymptotic properties depend on the distribution of the data. Large deviations from normality will result in sub-optimal estimates, or estimates that are distorted. If this is what she has in mind, then you can use robust PCA instead (cf. Candes et. al.)