2020
DOI: 10.1093/mnras/staa2900
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Fast estimation of aperture mass statistics – I. Aperture mass variance and an application to the CFHTLenS data

Abstract: We explore an alternative method to the usual shear correlation function approach for the estimation of aperture mass statistics in weak lensing survey data. Our approach builds on the direct estimator method. In this paper, to test and validate the methodology, we focus on the aperture mass dispersion. After computing the signal and noise for a weighted set of measured ellipticites we show how the direct estimator can be made into a linear order algorithm that enables a fast and efficient computation. We then… Show more

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Cited by 8 publications
(13 citation statements)
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“…In certain cases we might use further abbreviations, meaning that (𝑖 1 , ..., 𝑖 𝑛 ) 𝑁 ≡ (𝑖 1 , ..., 𝑖 𝑛 ) ≡ ≠. On applying the above estimator to the case of 𝑛 = 2, one can easily show that that this estimator is unbiased after averaging over the intrinsic ellipticity distribution, the galaxy positions within the aperture, and finally over cosmological ensembles (Schneider et al 1998;Porth et al 2020).…”
Section: Direct Estimators For the Aperture Mass Moments And Their Evaluation In Linear Order Timementioning
confidence: 99%
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“…In certain cases we might use further abbreviations, meaning that (𝑖 1 , ..., 𝑖 𝑛 ) 𝑁 ≡ (𝑖 1 , ..., 𝑖 𝑛 ) ≡ ≠. On applying the above estimator to the case of 𝑛 = 2, one can easily show that that this estimator is unbiased after averaging over the intrinsic ellipticity distribution, the galaxy positions within the aperture, and finally over cosmological ensembles (Schneider et al 1998;Porth et al 2020).…”
Section: Direct Estimators For the Aperture Mass Moments And Their Evaluation In Linear Order Timementioning
confidence: 99%
“…( 16) to determine the hierarchy of aperture mass moments, then this naive implementation would appear to result in an estimator that requires of the order 𝑁 𝑛 operations to compute. However, following our earlier work (Porth et al 2020), one can complete the sums to transform the estimators into sums and products of linear order terms. In Appendix A we explicitly show, using elementary means, how one can compute the skewness ( 𝑀 3 ap ) and kurtosis ( 𝑀 4 ap ) using linear sums.…”
Section: Direct Estimators For the Aperture Mass Moments And Their Evaluation In Linear Order Timementioning
confidence: 99%
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