  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.

Cosmology and Nongalactic Astrophysics