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Weak lensing statistics is typically measured as weighted sum of shearestimators or their products (shear-shear correlation). The weighting schemesare designed in the hope of minimizing the statistical error withoutintroducing systematic errors. It would be ideal to approach the Cramer-Raobound (the lower bound of the statistical uncertainty) in shear statistics,though it is generally difficult to do so in practice. The reasons may include:difficulties in galaxy shape measurement, inaccurate knowledge of theprobability-distribution-function (PDF) of the shear estimator,misidentification of point sources as galaxies, etc.. Using the shearestimators defined in Zhang et al. (2015), we show that one can overcome allthese problems, and allow shear measurement accuracy to approach the Cramer-Raobound. This can be achieved by symmetrizing the PDF of the shear estimator, orthe joint PDF of shear estimator pairs (for shear-shear correlation), withoutany prior knowledge of the PDF. Using simulated galaxy images, we demonstratethat under general observing conditions, this idea works as expected: itminimizes the statistical uncertainty without introducing systematic error.

Approaching the Cramer-Rao Bound in Weak Lensing with PDF Symmetrization