The Quasar Mass-Luminosity Plane III: Smaller Errors on Virial Mass
  Estimates
  We use 62185 quasars from the Sloan Digital Sky Survey (SDSS) DR5 sample to
explore the quasar mass-luminosity plane view of virial mass estimation.
Previous work shows deviations of ~0.4 dex between virial and reverberation
masses. The decline in quasar number density for the highest Eddington ratio
quasars at each redshift provides an upper bound of between 0.13 and 0.29 dex
for virial mass estimate statistical uncertainties. Across different redshift
bins, the maximum possible MgII mass uncertainties average 0.15 dex, while
H{\beta} uncertainties average 0.21 dex and CIV uncertainties average 0.27 dex.
Any physical spread near the high-Eddington-ratio boundary will produce a more
restrictive bound. A comparison of the sub-Eddington boundary slope using
H{\beta} and MgII masses finds better agreement with uncorrected MgII masses
than with recently proposed corrections. The best agreement for these bright
objects is produced by a multiplicative correction by a factor of 1.19, smaller
than the factor of 1.8 previously reported as producing the best agreement for
the entire SDSS sample.
