Techniques for Profile Binning and Analysis of Eigenvector Composite Spectra: Comparing Hβ and Mgiiλ2800 as Virial Estimators ✩ Jack W. Sulentic * Instituto de Astrof´ ısica de Andaluc´ ıa (CSIC), Granada, 18008, Espa˜ na Paola Marziani INAF, Osservatorio Astronomico di Padova, Padova,35122, Italia Ascensi´ on del Olmo and Ilse Plauchu-Frayn 1 Instituto de Astrof´ ısica de Andaluc´ ıa (CSIC), Granada, 18008, Espa˜ na Abstract We review the basic techniques for extracting information about quasar struc- ture and kinematics from the broad emission lines in quasars. We consider which lines can most effectively serve as virial estimators of black hole mass. At low redshift the Balmer lines,particularly broad Hβ , are the lines of choice. For redshifts greater than 0.7 – 0.8 one can follow Hβ into the IR windows or find an Hβ surrogate. We explain why UV Civλ1549 is not a safe virial estimator and how Mgiiλ2800 serves as the best virial surrogate for Hβ up to the highest redshift quasar known at z ≈ 7. We show how spectral bin- ning in a parameter space context (4DE1) makes possible a more effective comparison of Hβ and Mgii. It also helps to derive more accurate mass esti- mates from appropriately binned spectra and, finally, to map the dispersion in M BH and Eddington ratio across the quasar population. FWHM MgII is ✩ Invited talk presented on May 12, 2013 at the 9th SCSLSA held in Banja Koviliaˇ ca, Serbia. * Corresponding author Email addresses: sulentic@iaa.es (Jack W. Sulentic), paola.marziani@oapd.inaf.it (Paola Marziani) 1 Present address: IA-UNAM, Ensenada Campus, Ensenada, M´ exico Preprint submitted to Advances in Space Research November 13, 2018 arXiv:1310.4361v1 [astro-ph.CO] 16 Oct 2013