  Space-borne gravitational wave detectors like TianQin are expected to detect
gravitational wave signals emitted by the mergers of massive black hole
binaries. Luminosity distance information can be obtained from gravitational
wave observations, and one can perform cosmological inference if redshift
information can also be extracted, which would be straightforward if an
electro-magnetic counterpart exists. In this work, we concentrate on the
conservative scenario where the electro-magnetic counterparts are not
available, and comprehensively study if cosmological parameters can be inferred
through a statistical approach, utilizing the non-uniform distribution of
galaxies as well as the black hole mass-host galaxy bulge luminosity
relationship. By adopting different massive black hole binary merger models,
and assuming different detector configurations, we conclude that the
statistical inference of cosmological parameters is indeed possible. TianQin is
expected to constrain the Hubble constant to a relative error around 7%, and in
the most optimistic case, it is possible to achieve the level of 1.5%, if a
multi-detector network of TianQin and LISA is assumed. We find that without
electro-magnetic counterparts, all other cosmological parameters are poorly
constrained. However, in the optimistic case, where electro-magnetic
counterparts are available, one can constrain all cosmological parameters in
the standard Lambda cold dark matter cosmology. It is even possible to study
the evolution of equation of state for the dark energy.
