  In this paper we assess the relationship of the population of Active Galactic
Nuclei (AGN) selected by hard X-rays to the traditional population of AGN with
strong optical emission lines. First, we study the emission-line properties of
a new hard X-ray selected sample of 47 local AGN (classified optically as both
Type 1 and Type 2 AGN). We find that the hard X- ray (3-20 keV) and
[OIII]$\lambda$5007 optical emission-line luminosities are well-correlated over
a range of about four orders-of-magnitude in luminosity (mean luminosity ratio
2.15 dex with a standard deviation of $\sigma$ = 0.51 dex). Second, we study
the hard X-ray properties of a sample of 55 local AGN selected from the
literature on the basis of the flux in the [OIII] line. The correlation between
the hard X-ray (2-10 keV) and [OIII] luminosity for the Type 1 AGN is
consistent with what is seen in the hard X-ray selected sample. However, the
Type 2 AGN have a much larger range in the luminosity ratio, and many are very
weak in hard X-rays (as expected for heavily absorbed AGN). We then compare the
hard X-ray (3-20 keV) and [OIII] luminosity functions of AGN in the local
universe. These have similar faint-end slopes with a luminosity ratio of 1.60
dex (0.55 dex smaller than the mean value for individual hard X-ray selected
AGN). We conclude that at low redshift, selection by narrow optical emission-
lines will recover most AGN selected by hard X-rays (with the exception of BL
Lac objects). However, selection by hard X-rays misses a significant fraction
of the local AGN population with strong emission lines.
