  We study a regression characterization for the quadratic estimator of weak
lensing, developed by Hu and Okamoto (2001,2002), for cosmic microwave
background observations. This characterization motivates a modification of the
quadratic estimator by an adaptive Wiener filter which uses the robust Bayesian
techniques described in Strawderman (1971) and Berger (1980). This technique
requires the user to propose a fiducial model for the spectral density of the
unknown lensing potential but the resulting estimator is developed to be robust
to misspecification of this model. The role of the fiducial spectral density is
to give the estimator superior statistical performance in a "neighborhood of
the fiducial model" while controlling the statistical errors when the fiducial
spectral density is drastically wrong. Our estimate also highlights some
advantages provided by a Bayesian analysis of the quadratic estimator.
