Prediction intervals for regression models

This paper presents simple large sample prediction intervals for a future response Y(f) given a vector x(f) of predictors when the regression model has the form Y(i) = m(x(i)) + e(i) where m is a function of x(i) and the errors e(i) are iid. Intervals with correct asymptotic coverage and shortest asymptotic length can be made by applying the shorth estimator to the residuals. Since residuals underestimate the errors, finite sample correction factors are needed. As an application, three prediction intervals are given for the least squares multiple linear regression model. The asymptotic coverage and length of these intervals and the classical estimator are derived. The new intervals are useful since the distribution of the errors does not need to be known, and simulations suggest that the large sample theory often provides good approximations for moderate sample sizes. (c) 2006 Elsevier B.V. All rights reserved.