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In this note, we claim that diagonal scaling of a sample covariance matrix isasymptotically inconsistent if the ratio of the dimension to the sample sizeconverges to a positive constant, where population is assumed to be Gaussianwith a spike covariance model. Our non-rigorous proof relies on the replicamethod developed in statistical physics. In contrast to similar results knownin literature on principal component analysis, the strong inconsistency is notobserved. Numerical experiments support the derived formulas.

Inconsistency of diagonal scaling under high-dimensional limit: a replica approach