Improved Prediction Intervals and Distribution Functions

The plug-in solution is usually not entirely adequate for computing prediction intervals, as their coverage probability may differ substantially from the nominal value. Prediction intervals with improved coverage probability can be defined by adjusting the plug-in ones, using rather complicated asymptotic procedures or suitable simulation techniques. Other approaches are based on the concept of predictive likelihood for a future random variable. The contribution of this paper is the definition of a relatively simple predictive distribution function giving improved prediction intervals. This distribution function is specified as a first-order unbiased modification of the plug-in predictive distribution function based on the constrained maximum likelihood estimator. Applications of the results to the Gaussian and the generalized extreme-value distributions are presented. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.