Building Unbiased Estimators from Non-Gaussian Likelihoods with
  Application to Shear Estimation
  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. Both our first-order estimator and
Bernstein and Armstrong's estimator exhibit a bias which is quadratic in true
shear. Our third-order estimator is, at least in the realm of the toy problem
of Bernstein and Armstrong, unbiased to 0.1% in relative shear errors $\Delta
g/|g|$ for shears up to $|g|=0.2$.
