Prediction intervals for regression models

This paper presents simple large sample prediction intervals for a future response Yf given a vector xf of predictors when the regression model has the form Yi = m(xi) + ei where m is a function of xi and the errors ei 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 ∗David J. Olive is Associate Professor, Department of Mathematics, Southern Illinois University, Mailcode 4408, Carbondale, IL 62901-4408, USA. E-mail address: [email protected]. The author thanks the referees and editors for suggestions that improved the article.