  We use HII starburst galaxy apparent magnitude measurements to constrain
cosmological parameters in six cosmological models. A joint analysis of HII
galaxy, quasar angular size, baryon acoustic oscillations peak length scale,
and Hubble parameter measurements result in relatively model-independent and
restrictive estimates of the current values of the non-relativistic matter
density parameter $\Omega_{\rm m_0}$ and the Hubble constant $H_0$. These
estimates favor a 2.0$\sigma$ to 3.4$\sigma$ (depending on cosmological model)
lower $H_0$ than what is measured from the local expansion rate. The combined
data are consistent with dark energy being a cosmological constant and with
flat spatial hypersurfaces, but do not strongly rule out mild dark energy
dynamics or slightly non-flat spatial geometries.
