Cosmological model-independent test of $\mathrm{\Lambda }$CDM with two-point diagnostic by the observational Hubble parameter data

Aiming at exploring the nature of dark energy (DE), we use forty-three observational Hubble parameter data (OHD) in the redshift range $0 < z \leqslant 2.36$tomakeacosmologicalmodel-independenttestofthe$\Lambda$CDMmodelwithtwo-point$Omh^2(z_{2};z_{1})$diagnostic\mathrm{.}In$\Lambda$CDMmodel,withequationofstate(EoS)$w=-1$, two-point diagnostic relation $Om{h}^2\equiv {\mathrm{\Omega }}_m{h}^2$ is tenable, where ${\mathrm{\Omega }}_m$ is the present matter density parameter, and $h$ is the Hubble parameter divided by 100 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}\mathrm{M}\mathrm{p}{\mathrm{c}}^{-1}$. We utilize two methods: the weighted mean and median statistics to bin the OHD to increase the signal-to-noise ratio of the measurements. The binning methods turn out to be promising and considered to be robust. By applying the two-point diagnostic to the binned data, we find that although the best-fit values of $Om{h}^2$ fluctuate as the continuous redshift intervals change, on average, they are continuous with being constant within 1 $\sigma$ confidence interval. Therefore, we conclude that the $\mathrm{\Lambda }$CDM model cannot be ruled out.