Neural-network selection of high-redshift radio quasars, and the
  luminosity function at z~4
  We obtain a sample of 87 radio-loud QSOs in the redshift range 3.6<z<4.4 by
cross-correlating sources in the FIRST radio survey S{1.4GHz} > 1 mJy with
star-like objects having r <20.2 in SDSS Data Release 7. Of these 87 QSOs, 80
are spectroscopically classified in previous work (mainly SDSS), and form the
training set for a search for additional such sources. We apply our selection
to 2,916 FIRST-DR7 pairs and find 15 likely candidates. Seven of these are
confirmed as high-redshift quasars, bringing the total to 87. The candidates
were selected using a neural-network, which yields 97% completeness (fraction
of actual high-z QSOs selected as such) and an efficiency (fraction of
candidates which are high-z QSOs) in the range of 47 to 60%. We use this sample
to estimate the binned optical luminosity function of radio-loud QSOs at $z\sim
4$, and also the LF of the total QSO population and its comoving density. Our
results suggest that the radio-loud fraction (RLF) at high z is similar to that
at low-z and that other authors may be underestimating the fraction at high-z.
Finally, we determine the slope of the optical luminosity function and obtain
results consistent with previous studies of radio-loud QSOs and of the whole
population of QSOs. The evolution of the luminosity function with redshift was
for many years interpreted as a flattening of the bright end slope, but has
recently been re-interpreted as strong evolution of the break luminosity for
high-z QSOs, and our results, for the radio-loud population, are consistent
with this.
