  A significant proportion ($\sim30\%$) of the short-duration gamma-ray bursts
(SGRBs) localised by Swift have no detected host galaxy coincident with the
burst location to deep limits, and also no high-likelihood association with
proximate galaxies on the sky. These SGRBs may represent a population at
moderately high redshifts ($z\gtrsim1$), for which the hosts are faint, or a
population where the progenitor has been kicked far from its host or is sited
in an outlying globular cluster. We consider the afterglow and host
observations of three 'hostless' bursts (GRBs 090305A, 091109B and 111020A),
coupled with a new observational diagnostic to aid the association of SGRBs
with putative host galaxies to investigate this issue. Considering the well
localised SGRB sample, 7/25 SGRBs can be classified as 'hostless' by our
diagnostic. Statistically, however, the proximity of these seven SGRBs to
nearby galaxies is higher than is seen for random positions on the sky. This
suggests that the majority of 'hostless' SGRBs have likely been kicked from
proximate galaxies at moderate redshift. Though this result still suggests only
a small proportion of SGRBs will be within the AdLIGO horizon for NS-NS or
NS-BH inspiral detection ($z\sim0.1$), in the particular case of GRB 111020A a
plausible host candidate is at $z=0.02$.
