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Weak gravitational lensing analyses are fundamentally limited by the intrinsic, non-Gaussian distribution of galaxy shapes. We explore alternative statistics for samples of ellipticity measurements that are unbiased, efficient, and robust. We take the non-linear mapping of gravitational shear and the effect of noise into account. We then discuss how the distribution of individual galaxy shapes in the observed field of view can be modeled by fitting Fourier modes to the shear pattern directly. We simulated samples of galaxy ellipticities, using both theoretical distributions and real data for ellipticities and noise. We determined the possible bias $Delta e$, the efficiency $eta$ and the robustness of the least absolute deviations, the biweight, and the convex hull peeling estimators, compared to the canonical weighted mean. Using these statistics for regression, we have shown the applicability of direct Fourier mode fitting. These estimators can be unbiased in the absence of noise, and decrease noise bias by more than $sim 30%$. The convex hull peeling estimator distribution is centered around the underlying shear, and its bias least affected by noise. The least absolute deviations estimator to be the most efficient estimator in almost all cases, except in the Gaussian case, where its still competitive ($0.83<eta <5.1$) and therefore robust. These results hold when fitting Fourier modes, where amplitudes of variation in ellipticity are determined to the order of $10^{-3}$. The peak of the ellipticity distribution is a direct tracer of the underlying shear and unaffected by noise, and we have shown that estimators that are sensitive to a central cusp perform more efficiently, potentially reducing uncertainties by more than $50%$ and significantly decreasing noise bias.
Upcoming weak-lensing surveys have the potential to become leading cosmological probes provided all systematic effects are under control. Recently, the ejection of gas due to feedback energy from active galactic nuclei (AGN) has been identified as ma
The statistics of shear peaks have been shown to provide valuable cosmological information beyond the power spectrum, and will be an important constraint of models of cosmology with the large survey areas provided by forthcoming astronomical surveys.
We study the statistics of peaks in a weak lensing reconstructed mass map of the first 450 square degrees of the Kilo Degree Survey. The map is computed with aperture masses directly applied to the shear field with an NFW-like compensated filter. We
NonGaussian cosmic shear statistics based on weak-lensing aperture mass ($M_{rm ap}$) maps can outperform the classical shear two-point correlation function ($gamma$-2PCF) in terms of cosmological constraining power. However, reaching the full potent
In this paper, we analyze in detail with numerical simulations how the mask effect can influence the weak lensing peak statistics reconstructed from the shear measurement of background galaxies. It is found that high peak fractions are systematically