  Massively multiplexed spectrographs will soon gather large statistical
samples of stellar spectra. The accurate estimation of uncertainties on derived
parameters, such as line-of-sight velocity $v_\mathrm{los}$, especially for
spectra with low signal-to-noise ratios, is paramount. We generated an ensemble
of simulated optical spectra of stars as if they were observed with low- and
medium-resolution fiber-fed instruments on an 8-meter class telescope, similar
to the Subaru Prime Focus Spectrograph, and determined $v_\mathrm{los}$ by
fitting stellar templates to the simulations. We compared the empirical errors
of the derived parameters -- calculated from an ensemble of simulations -- to
the asymptotic error determined from the Fisher matrix, as well as from Monte
Carlo sampling of the posterior probability. We confirm that the uncertainty of
$v_\mathrm{los}$ scales with the inverse square root of $S/N$, but also show
how this scaling breaks down at low $S/N$ and analyze the error and bias caused
by template mismatch. We outline a computationally optimized algorithm to fit
multi-exposure data and provide the mathematical model of stellar spectrum
fitting that maximizes the so called significance, which allows for calculating
the error from the Fisher matrix analytically. We also introduce the effective
line count, and provide a scaling relation to estimate the error of
$v_\mathrm{los}$ measurement based on the stellar type. Our analysis covers a
range of stellar types with parameters that are typical of the Galactic outer
disk and halo, together with analogs of stars in M31 and in satellite dwarf
spheroidal galaxies around the Milky Way.
