用PDF对称化逼近弱透镜的Cramer-Rao界
Approaching the Cramer-Rao Bound in Weak Lensing with PDF Symmetrization
摘要：
弱透镜统计量通常被测量为剪切估计量的加权和或它们的乘积（剪切-剪切相关）。加权方案的设计是希望在不引入系统误差的情况下使统计误差最小化。在剪切统计中接近克拉美-拉奥界（统计不确定性的下限）是理想的，尽管在实践中通常很难做到。原因可能包括：在星系形状测量的困难，不准确的知识的概率分布函数（PDF）的剪切估计，错误识别的点源作为星系，等等。使用Zhang等人（2015）中定义的剪切估计量，我们证明可以克服所有这些问题，并允许剪切测量精度接近Cramer-Rao界。这可以通过对称化剪切估计器的PDF或剪切估计器对的联合PDF（用于剪切-剪切相关性）来实现，而无需PDF的任何先验知识。使用模拟的星系图像，我们表明，在一般的观测条件下，这种想法的工作原理如预期的那样：它最大限度地减少了统计不确定性，而不引入系统误差。
英文摘要：
Weak lensing statistics is typically measured as weighted sum of shear estimators or their products (shear-shear correlation). The weighting schemes are designed in the hope of 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-function (PDF) of the shear estimator, misidentification of point sources as galaxies, etc.. Using the shear estimators defined in Zhang et al. (2015), we show that one can overcome all 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
