The Multi-Tracer Optimal Estimator applied to VIPERS
  We use mock galaxy data from the VIMOS Public Extragalactic Redshift Survey
(VIPERS) to test the performance of the Multi-Tracer Optimal Estimator (MTOE)
of Abramo et al. as a tool to measure the monopoles of the power spectra of
multiple tracers of the large-scale structure, $P^{(0)}_\alpha(k)$. We show
that MTOE provides more accurate measurements than the standard technique of
Feldman, Kaiser & Peacock (FKP), independently of the tracer-selection strategy
adopted, on both small and large scales. The largest improvements on individual
$P^{(0)}_\alpha(k)$ are obtained using a colour-magnitude selection on small
scales, due to MTOE being naturally better equipped to deal with shot noise: we
report an average error reduction with respect to FKP of $\sim$ 40$\%$ at $k \,
[h$ Mpc$^{-1}]\gtrsim 0.3$. On large scales ($k[h$ Mpc$^{-1}]\lesssim0.1$), the
gain in accuracy resulting from cosmic-variance cancellation is $\sim$ 10$\%$
for the ratios of $P^{(0)}_\alpha(k)$. We have carried out a Monte-Carlo Markov
Chain analysis to determine the impact of these gains on several quantities
derived from $P^{(0)}_\alpha(k)$. If we push the measurement to scales $0.3 < k
\, [h$ Mpc$^{-1}]< 0.5$, the average improvements are $\sim$ 30 $\%$ for the
amplitudes of the monopoles, $\sim$ 70 $\%$ for the monopole ratios, and $\sim$
20 $\%$ for the galaxy biases. Our results highlight the potential of MTOE to
shed light upon the physics that operate both on large and small cosmological
scales. The effect of MTOE on cosmological constraints using VIPERS data will
be addressed in a separate paper.
