Approximate maximum entropy on the mean for instrumental variable regression

We want to estimate an unknown finite measure mu(x) from a noisy observation of generalized moments of mu(x), defined as the integral of a continuous function Phi with respect to mu(x). Assuming that only a quadratic approximation Phi(m) available, we define an approximate maximum entropy solution as a minimizer of a convex functional subject to a sequence of convex constraints. We establish asymptotic properties of the approximate solution under regularity assumptions on the convex functional, and we study an application of this result to instrumental variable estimation. (c) 2012 Elsevier B.V. All rights reserved.