Optimal Prediction in Loglinear Models

This paper introduces a Laplace inversion technique for deriving unbiased predictors in exponential families. This general technique is applied to derive the exact optimal unbiased predictor in loglinear models with Gaussian disturbances under quadratic loss. An exact unbiased estimator for its variance is also derived. The result generalizes earlier work and unifies expressions in terms of a simple hypergeometric function which has a number of advantages. Nonlinear models rarely admit exact solutions and we therefore compare the exact predictor with other predictors commonly used in nonlinear models. The naive predictor which is biased and inconsistent, can be best in terms of mean squared error, even for sample sizes of up to 40.