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Asymptotic Likelihood-Based Prediction Functions
Thomas F. Cooley
William R. Parke
Abstract
This paper develops asymptotic prediction functions that approximate the shape of the density of future observations and correct for parameter uncertainty. The functions are based on extensions to a definition of predictive likelihood originally suggested by Lauritzen and Hinkley. The prediction function is shown to possess efficiency properties based on the Kullback-Leibler measure of information loss. Examples of the application of the prediction function and the derivation of relative efficiency are shown for linear normal models, nonnormal models, and ARCH models.
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