Building Unbiased Estimators from Non-Gaussian Likelihoods with Application to Shear Estimation

Understand

We develop a general framework for generating estimators of a given quantity which are unbiased to a given order in the difference between the true value of the underlying quantity and the fiducial position in theory space around which we expand the likelihood.

• We apply this formalism to rederive the optimal quadratic estimator and show how the replacement of the second derivative matrix with the Fisher matrix is a generic way of creating an unbiased estimator (assuming choice of the fiducial model is independent of data).
• Next apply the approach to estimation of shear lensing, closely following the work of Bernstein and Armstrong (2014).
• Our first order estimator reduces to their estimator in the limit of zero shear, but it also naturally allows for the case of non-constant shear and the easy calculation of correlation functions or power spectra using standard methods.