Maximum Entropy Approximations for Asymptotic Distributions of Smooth Functions of Sample Means

We propose an information-theoretic approach to approximate asymptotic distributions of statistics using the maximum entropy (ME) densities. Conventional ME densities are typically defined on a bounded support. For distributions defined on unbounded supports, we use an asymptotically negligible dampening function for the ME approximation such that it is well defined on the real line. We establish order n^-1 asymptotic equivalence between the proposed method and the classical Edgeworth approximation for general statistics that are smooth functions of sample means. Numerical examples are provided to demonstrate the efficacy of the proposed method.