  We present MgII-based black hole mass estimates for 27,602 quasars with
rest-frame UV spectra available in the Sloan Digital Sky Survey Data Release
Three. This estimation is possible due to the existence of an empirical
correlation between the radius of the broad line region and the continuum
luminosity at 3000 Angstroms. We regenerate this correlation by applying our
measurement method to UV spectra of low-redshift quasars in the HST/IUE
databases which have corresponding reverberation mapping estimates of the Hbeta
broad line region's radius. Our mass estimation method uses the line dispersion
rather than the full width at half maximum of the low-ionization MgII emission
line. We measure MgII line dispersions for quasars whose spectra have been
reconstructed using the most significant eigenspectra produced through
Principal Component Analysis. We have tested the reliability of using
reconstructed spectra in black hole mass estimation using a Monte Carlo
simulation and by comparing the results from original and reconstructed Data
Release Three spectra. We show that using reconstructed spectra not only makes
bias-free mass estimation possible for quasars with low spectroscopic
signal-to-noise ratio, but also reduces the intrinsic scatter of the
distribution of the black hole masses to lower than 0.15 dex.
