Unbiased contaminant removal for 3D galaxy power spectrum measurements
  We assess and develop techniques to remove contaminants when calculating the
3D galaxy power spectrum. We separate the process into three separate stages:
(i) removing the contaminant signal, (ii) estimating the uncontaminated
cosmological power spectrum, (iii) debiasing the resulting estimates. For (i),
we show that removing the best-fit contaminant mode subtraction), and setting
the contaminated components of the covariance to be infinite (mode
deprojection) are mathematically equivalent. For (ii), performing a Quadratic
Maximum Likelihood (QML) estimate after mode deprojection gives an optimal
unbiased solution, although it requires the manipulation of large $N_{\rm
mode}^2$ matrices ($N_{\rm mode}$ being the total number of modes)}, which is
unfeasible for recent 3D galaxy surveys. Measuring a binned average of the
modes for (ii) as proposed by \citet*[FKP]{Feldman} is faster and simpler, but
is sub-optimal and gives rise to a biased solution. We present a method to
debias the resulting FKP measurements that does not require any large matrix
calculations. We argue that the sub-optimality of the FKP estimator compared
with the QML estimator, caused by contaminants is less severe than that
commonly ignored due to the survey window.
