  With the forthcoming release of high precision polarization measurements,
such as from the Planck satellite, it becomes critical to evaluate the
performance of estimators for the polarization fraction and angle. These two
physical quantities suffer from a well-known bias in the presence of
measurement noise, as has been described in part I of this series. In this
paper, part II of the series, we explore the extent to which various estimators
may correct the bias. Traditional frequentist estimators of the polarization
fraction are compared with two recent estimators: one inspired by a Bayesian
analysis and a second following an asymptotic method. We investigate the
sensitivity of these estimators to the asymmetry of the covariance matrix which
may vary over large datasets. We present for the first time a comparison among
polarization angle estimators, and evaluate the statistical bias on the angle
that appears when the covariance matrix exhibits effective ellipticity. We also
address the question of the accuracy of the polarization fraction and angle
uncertainty estimators. The methods linked to the credible intervals and to the
variance estimates are tested against the robust confidence interval method.
From this pool of estimators, we build recipes adapted to different use-cases:
build a mask, compute large maps, and deal with low S/N data. More generally,
we show that the traditional estimators suffer from discontinuous distributions
at low S/N, while the asymptotic and Bayesian methods do not. Attention is
given to the shape of the output distribution of the estimators, and is
compared with a Gaussian. In this regard, the new asymptotic method presents
the best performance, while the Bayesian output distribution is shown to be
strongly asymmetric with a sharp cut at low S/N.Finally, we present an
optimization of the estimator derived from the Bayesian analysis using adapted
priors.
