Updated constraints on $f(T)$ models using direct and indirect measurements of the Hubble parameter

We extract observational constraints on $f(T)$ gravity, using the recently proposed statistical method which is not affected by the value of $H_0$ and thus it bypasses the problem of the disagreement in its exact numerical value between Planck and direct measurements. We use direct measurements of the Hubble parameter with the corresponding covariance matrix, and for completeness we perform a joint analysis using the latest data from Supernovae type Ia based on JLA sample, quasi-stellar objects, and Cosmic Microwave Background shift parameter from Planck. We analyze a large family of $f(T)$ models, and we compare the fitting results with $\Lambda$CDM cosmology using the AIC statistical test. Utilizing only the Hubble parameter data we find that in the case of the power-law $f(T)$ model a small but non-zero deviation from $\Lambda$CDM cosmology is slightly favored at 1-$\sigma$, nevertheless the corresponding AIC value shows a statistical equivalence with it. Finally, the join analysis reveals that all $f(T)$ models are very efficient and in very good agreement with observations.