Statistical analysis with cosmic-expansion-rate measurements and
  two-point diagnostics
  Direct measurements of Hubble parameters $H(z)$ are very useful for
cosmological model parameters inference. Based on them, Sahni, Shafieloo and
Starobinski introduced a two-point diagnostic $Omh^2(z_i, z_j)$ as an
interesting tool for testing the validity of the $\Lambda$CDM model. Applying
this test they found a tension between observations and predictions of the
$\Lambda$CDM model. We use the most comprehensive compilation $H(z)$ data from
baryon acoustic oscillations (BAO) and differential ages (DA) of passively
evolving galaxies to study cosmological models using the Hubble parameters
itself and to distinguish whether $\Lambda$CDM model is consistent with the
observational data with statistical analysis of the corresponding $Omh^2(z_i,
z_j)$ two-point diagnostics. Our results show that presently available $H(z)$
data significantly improve the constraints on cosmological parameters. The
corresponding statistical $Omh^2(z_i, z_j)$ two-point diagnostics seems to
prefer the quintessence with $w>-1$ over the $\Lambda$CDM model. Better and
more accurate prior knowledge of the Hubble constant, will considerably improve
the performance of the statistical $Omh^2(z_i, z_j)$ method.
