title: Comparison of eigeninference based on one- and two-point Green's functions.
abstract: We compare two methods of eigeninference from large sets of data. Our analysis points at the superiority of our eigeninference method based on one-point Green's functions and Padé approximants over a method based on fluctuations and two-point Green's functions. The first method is orders of magnitude faster than the second one; moreover, we found a source of potential instability of the second method and identified it as arising from the spurious zero and negative modes of the estimator for the variance operator of a certain multidimensional Gaussian distribution, inherent for that method. We also present eigeninference based on spectral moments of negative orders, for strictly positive spectra. Finally, we compare the cases of eigeninference of real-valued and complex-valued correlated Wishart distributions, reinforcing our conclusions on the advantage of the one-point Green's function method.
authors.affiliation: M. Smoluchowski Institute of Physics, Jagiellonian University, S. Łojasiewicza 11, 30-348 Cracow, Poland.
authors.forename: Zbigniew
authors.initials: Z
authors.lastname: Drogosz
authors.affiliation: M. Smoluchowski Institute of Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, S. Łojasiewicza 11, 30-348 Cracow, Poland.
authors.forename: Jerzy
authors.initials: J
authors.lastname: Jurkiewicz
authors.affiliation: M. Smoluchowski Institute of Physics, Jagiellonian University, S. Łojasiewicza 11, 30-348 Cracow, Poland.
authors.forename: Grzegorz
authors.initials: G
authors.lastname: Łukaszewski
authors.affiliation: M. Smoluchowski Institute of Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, S. Łojasiewicza 11, 30-348 Cracow, Poland.
authors.forename: Maciej A
authors.initials: MA
authors.lastname: Nowak