A novel estimator of the polarization amplitude from normally
  distributed Stokes parameters
  We propose a novel estimator of the polarization amplitude from a single
measurement of its normally distributed $(Q,U)$ Stokes components. Based on the
properties of the Rice distribution and dubbed 'MAS' (Modified ASymptotic), it
meets several desirable criteria:(i) its values lie in the whole positive
region; (ii) its distribution is continuous; (iii) it transforms smoothly with
the signal-to-noise ratio (SNR) from a Rayleigh-like shape to a Gaussian one;
(iv) it is unbiased and reaches its components' variance as soon as the SNR
exceeds 2; (v) it is analytic and can therefore be used on large data-sets. We
also revisit the construction of its associated confidence intervals and show
how the Feldman-Cousins prescription efficiently solves the issue of classical
intervals lying entirely in the unphysical negative domain. Such intervals can
be used to identify statistically significant polarized regions and conversely
build masks for polarization data. We then consider the case of a general
$[Q,U]$ covariance matrix and perform a generalization of the estimator that
preserves its asymptotic properties. We show that its bias does not depend on
the true polarization angle, and provide an analytic estimate of its variance.
The estimator value, together with its variance, provide a powerful
point-estimate of the true polarization amplitude that follows an unbiased
Gaussian distribution for a SNR as low as 2. These results can be applied to
the much more general case of transforming any normally distributed random
variable from Cartesian to polar coordinates.
