  The speed of gravitational waves $v_g$ can be measured with the time delay
between gravitational-wave detectors. Our study provides a more precise
measurement of $v_g$ using gravitational-wave signals only, compared with
previous studies. We select 52 gravitational-wave events that were detected
with high confidence by at least two detectors in the first three observing
runs (O1, O2, and O3) of Advanced LIGO and Advanced Virgo. We use Markov chain
Monte Carlo and nested sampling to estimate the $v_g$ posterior distribution
for each of those events. We then combine their posterior distributions to find
the 90% credible interval of the combined $v_g$ distribution for which we
obtain $0.99^{+0.02}_{-0.02}c$ without the use of more accurate sky
localization from the electromagnetic signal associated with GW170817.
Restricting attention to the 50 binary black hole events generates the same
result, while the use of the electromagnetic sky localization for GW170817
gives a tighter constraint of $0.99^{+0.01}_{-0.02}c$. The abundance of
gravitational wave events allows us to apply hierarchical Bayesian inference on
the posterior samples to simultaneously constrain all nine coefficients for
Lorentz violation in the nondispersive, nonbirefringent limit of the
gravitational sector of the Standard-Model Extension test framework. We compare
the hierarchical Bayesian inference method with other methods of combining
limits on Lorentz violation in the gravity sector that are found in the
literature.
