The Hubble constant (${H}_{0}$ ) is a measurement to describe the expansion rate
of the Universe in the current era. However, there is a $4.4\sigma $ discrepancy
between the measurements from the early Universe and the late Universe. In this
research, we propose a model-free and distance-free method to constrain
${H}_{0}$ . Combining Friedman-Lema\^itre-Robertson-Walker cosmology with
geometrical relation of the proper motion of extragalactic jets, the lower
limit (${H}_{0,\mathrm{m}\mathrm{i}\mathrm{n}}$ ) of ${H}_{0}$ can be determined using only three
cosmology-free observables: the redshifts of the host galaxies, as well as the
approaching and receding angular velocities of radio jets. Using these, we
propose to use the Kolmogorov-Smirnov test (K-S test) between cumulative
distribution functions of ${H}_{0,\mathrm{m}\mathrm{i}\mathrm{n}}$ to differentiate cosmology. We
simulate 100, 200, and 500 extragalactic jets with 3 levels of accuracy of the
proper motion (${\mu}_{a}$ and ${\mu}_{r}$ ), at $10\mathrm{\%}$ , $5\mathrm{\%}$ , and $1\mathrm{\%}$ ,
corresponding to the accuracies of the current and future radio
interferometers. We perform K-S tests between the simulated samples as
theoretical distributions with different ${H}_{0}$ and power-law index of
velocity distribution of jets and mock observational data. Our result suggests
increasing sample sizes leads to tighter constraints on both power-law index
and the Hubble constant at moderate accuracy (i.e., $10\mathrm{\%}$ and $5\mathrm{\%}$ ) while at
$1\mathrm{\%}$ accuracy, increasing sample sizes leads to tighter constraints on
power-law index more. Improving accuracy results in better constraints in the
Hubble constant compared with the power-law index in all cases but it
alleviates the degeneracy.