Prediction interval estimation in transformed linear models

Abstract

We study the prediction problem for a future response in the original scale when the Box–Cox transformation is applied to a multiple regression problem. We proceed by the usual method of estimating the transformation parameter, constructing a prediction interval for the transformed future value, and then inverting the transformation. Conditions are determined which ensure that these prediction intervals have correct coverage probability for large sample size. Simulation results are presented to verify the accuracy of the nominal coverage probabilities.