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This paper applies the recently axiomatized Optimum Information Principle(minimize the Kullback-Leibler information subject to all relevant information)to nonparametric density estimation, which provides a theoretical foundation aswell as a computational algorithm for maximum entropy density estimation. Theestimator, called optimum information estimator, approximates the true densityarbitrarily well. As a by-product I obtain a measure of goodness of fit ofparametric models (both conditional and unconditional) and an absolutecriterion for model selection, as opposed to other conventional methods such asAIC and BIC which are relative measures.

An Information-Theoretic Approach to Nonparametric Estimation, Model Selection, and Goodness of Fit