  We examine the possibility that the observed relation between black-hole mass
and host-galaxy stellar velocity dispersion (the M-sigma relation) is biased by
an observational selection effect, the difficulty of detecting a black hole
whose sphere of influence is smaller than the telescope resolution. In
particular, we critically investigate recent claims that the M-sigma relation
only represents the upper limit to a broad distribution of black-hole masses in
galaxies of a given velocity dispersion. We find that this hypothesis can be
rejected at a high confidence level, at least for the early-type galaxies with
relatively high velocity dispersions (median 268 km/s) that comprise most of
our sample. We also describe a general procedure for incorporating
observational selection effects in estimates of the properties of the M-sigma
relation. Applying this procedure we find results that are consistent with
earlier estimates that did not account for selection effects, although with
larger error bars. In particular, (i) the width of the M-sigma relation is not
significantly increased; (ii) the slope and normalization of the M-sigma
relation are not significantly changed; (iii) most or all luminous early-type
galaxies contain central black holes at zero redshift. Our results may not
apply to late-type or small galaxies, which are not well-represented in our
sample.
