  An empirical relationship, of particular interest for studies of high
redshift active galactic nuclei (AGNs) and quasars, between the masses of their
central black-holes and rest-frame ultraviolet (UV) parameters measured in
single-epoch AGN spectra is presented. This relationship is calibrated to
recently measured reverberation masses of low-redshift AGNs and quasars. An
empirical relationship between single-epoch rest-frame optical
spectrophotometric measurements and the central masses is also presented. The
UV relationship allows reasonable estimates of the central masses to be made of
high-redshift AGNs and quasars for which these masses cannot be directly or
easily measured by the techniques applicable to the lower luminosity, nearby
AGNs. The central mass obtained by this method can be estimated to within a
factor of ~3 for most objects. This is reasonable given the intrinsic
uncertainty of a factor less than 2 in the primary methods used to measure the
central masses of nearby inactive and active galaxies, namely resolved gas and
stellar kinematics in the underlying host galaxy and reverberation-mapping
techniques. The UV relationship holds good potential for being a powerful tool
to study black-hole demographics at high redshift as well as to statistically
study the fundamental properties of AGNs. The broad line region size -
luminosity relationship is key to the calibrations presented here. The fact
that its intrinsic scatter is also the main source of uncertainty in the
calibrations stresses the need for better observational constraints to be
placed on this relationship. The empirically calibrated relationships presented
here will be applied to quasar samples in forthcoming work.
