  We investigate the observational constraints on the interacting holographic
dark energy model. We consider five typical interacting models with the
interaction terms $Q=3\beta H\rho_{\rm{de}}$, $Q=3\beta H\rho_{\rm{c}}$,
$Q=3\beta H(\rho_{\rm{de}}+\rho_{\rm c})$, $Q=3\beta
H\sqrt{\rho_{\rm{de}}\rho_{\rm c}}$, and $Q=3\beta
H\frac{\rho_{\rm{de}}\rho_{c}}{\rho_{\rm{de}}+\rho_{\rm c}}$, respectively,
where $\beta$ is a dimensionless coupling constant. The observational data we
use in this paper include the JLA compilation of type Ia supernovae data, the
Planck 2015 distance priors data of cosmic microwave background observation,
the baryon acoustic oscillations measurements, and the Hubble constant direct
measurement. We make a comparison for these five interacting holographic dark
energy models by employing the information criteria, and we find that, within
the framework of holographic dark energy, the $Q=3\beta
H\frac{\rho_{\rm{de}}\rho_{\rm c}}{\rho_{\rm{ de}}+\rho_{\rm c}}$ model is most
favored by current data, and the $Q=3\beta H\rho_{\rm c}$ model is relatively
not favored by current data. For the $Q=3\beta H\rho_{\rm{de}}$ and $Q=3\beta
H\frac{\rho_{\rm{de}}\rho_{\rm c}}{\rho_{\rm{ de}}+\rho_{\rm c}}$ models, a
positive coupling $\beta$ can be detected at more than 2$\sigma$ significance.
