  Based on the measured sizes of broad line region of the reverberation-mapping
AGN sample, two new empirical relations are introduced to estimate the central
black hole masses of radio-loud high-redshift ($z > 0.5$) AGNs. First, using
the archival $IUE/HST$ spectroscopy data at UV band for the
reverberation-mapping objects, we obtained two new empirical relations between
the BLR size and \Mg/\C emission line luminosity. Secondly, using the newly
determined black hole masses of the reverberation-mapping sample for
calibration, two new relationships for determination of black hole mass with
the full width of half maximum and the luminosity of \Mg/\C line are also
found. We then apply the relations to estimate the black hole masses of AGNs in
Large Bright Quasar Surveyq and a sample of radio-loud quasars. For the objects
with small radio-loudness, the black hole mass estimated using the $R_{\rm BLR}
- L_{\eMg/\eC}$ relation is consistent with that from the $R_{BLR} -
L_{3000\AA/1350 \AA}$ relation. But for radio-loud AGNs, the mass estimated
from the $R_{BLR} - L_{\eMg/\eC}$ relation is systematically lower than that
from the continuum luminosity $L_{3000\AA/1350\AA}$. Because jets could have
significant contributions to the UV/optical continuum luminosity of radio-loud
AGNs, we emphasized again that for radio-loud AGNs, the emission line
luminosity may be a better tracer of the ionizing luminosity than the continuum
luminosity, so that the relations between the BLR size and UV emission line
luminosity should be used to estimate the black hole masses of high redshift
radio-loud AGNs.
