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We compare two methods of eigen-inference from large sets of data, based onthe analysis of one-point and two-point Green's functions, respectively. Ouranalysis points at the superiority of eigen-inference based on one-pointGreen's function. First, the applied by us method based on Pad?e approximantsis orders of magnitude faster comparing to the eigen-inference based onuctuations (two-point Green's functions). Second, we have identified the sourceof potential instability of the two-point Green's function method, as arisingfrom the spurious zero and negative modes of the estimator for a varianceoperator of the certain multidimensional Gaussian distribution, inherent forthe two-point Green's function eigen-inference method. Third, we have presentedthe cases of eigen-inference based on negative spectral moments, for strictlypositive spectra. Finally, we have compared the cases of eigen-inference ofreal-valued and complex-valued correlated Wishart distributions, reinforcingour conclusions on an advantage of the one-point Green's function method.

Signal from noise retrieval from one and two-point Green's function - comparison