Predictive Intervals Based on Reuse of the Sample

A general method is presented for constructing a predictive interval (PI) of specified content for a future observation. This construction is based on a cross-validation or sample reuse methodology that makes use of a one-at-a-time schema of observational omissions. By starting with a prespecified class of PI's, this methodology can be used to select the “best” PI in the class. This has been done for a variety of classes of PI's for location and multiple regression models. The coverage properties of certain “best” intervals are considered by Monte Carlo and large sample techniques.