Avoiding bias in reconstructing the largest observable scales from
  partial-sky data
  Obscuration due to Galactic emission complicates the extraction of
information from cosmological surveys, and requires some combination of the
(typically imperfect) modeling and subtraction of foregrounds, or the removal
of part of the sky. This particularly affects the extraction of information
from the largest observable scales. Maximum-likelihood estimators for
reconstructing the full-sky spherical harmonic coefficients from partial-sky
maps have recently been shown to be susceptible to contamination from within
the sky cut, arising due to the necessity to band-limit the data by smoothing
prior to reconstruction. Using the WMAP 7-year data, we investigate modified
implementations of such estimators which are robust to the leakage of
contaminants from within masked regions. We provide a measure, based on the
expected amplitude of residual foregrounds, for selecting the most appropriate
estimator for the task at hand. We explain why the related quadratic
maximum-likelihood estimator of the angular power spectrum does not suffer from
smoothing-induced bias.
