APPROACHING THE CRAMER-RAO BOUND IN WEAK LENSING WITH PDF SYMMETRIZATION

作者：Zhang, Jun^*; Zhang, Pengjie; Luo, Wentao

来源：Astrophysical Journal, 2017, 834(1): 8.

DOI：10.3847/1538-4357/834/1/8

• gravitational lensing: weak
• large-scale structure of universe
• methods: data analysis
• techniques: image processing

Weak lensing statistics is typically measured as the weighted sum of shear estimators or their products (shear-shear correlation). The weighting schemes are designed with a view to minimizing the statistical error without introducing systematic errors. It would be ideal to approach the Cramer-Rao bound (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 the probability distribution PDF) of the shear estimator, misidentification of point sources as galaxies, etc. Using the shear estimators defined by Zhang et al., we show that one can overcome these problems, and allow shear measurement accuracy to approach the Cramer-Rao bound. This can be achieved by symmetrizing the PDF of the shear estimator, or the joint PDF of shear estimator pairs (for shear-shear correlation), without any prior knowledge of the PDF. Using simulated galaxy images, we demonstrate that under general observing conditions, this idea works as expected: it minimizes the statistical uncertainty without introducing systematic error.

• 出版日期2017-1-1
• 单位上海交通大学; 中国科学院上海天文台