The variance of the locally measured Hubble parameter explained with
  different estimators
  We study the expected variance of measurements of the Hubble constant, $H_0$,
as calculated in either linear perturbation theory or using non-linear velocity
power spectra derived from $N$-body simulations. We compare the variance with
that obtained by carrying out mock observations in the N-body simulations, and
show that the estimator typically used for the local Hubble constant in studies
based on perturbation theory is different from the one used in studies based on
N-body simulations. The latter gives larger weight to distant sources, which
explains why studies based on N-body simulations tend to obtain a smaller
variance than that found from studies based on the power spectrum. Although
both approaches result in a variance too small to explain the discrepancy
between the value of $H_0$ from CMB measurements and the value measured in the
local universe, these considerations are important in light of the percent
determination of the Hubble constant in the local universe.
