Information Theoretic Asymptotic Approximations for Distributions of Statistics
نویسندگان
چکیده
We propose an information theoretic approach to approximating asymptotic distributions of statistics using the maximum entropy densities. Conventional maximum entropy densities are typically defined on a bounded support. For distributions defined on unbounded supports, we propose to use an asymptotically negligible dampening function for the maximum entropy 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 expansion for general statistics that are smooth functions of sample means. Numerical examples are provided to demonstrate the efficacy of the proposed method.
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