RESAMPLING PROCEDURES IN LINEAR MODELS

Abstract

We will study here different resampling procedures for creating confidence sets in linear models. A special technique called abstract resampling makes it possible to use the true residuals and the true model for resampling. This may seem to be peculiar since the true residuals contains unknown parameters and thus are non observable; but for each specified parameter value the residuals are observable and can be used for resampling. Furthermore simulating the null distribution of some appropriate statistic gives the possibility to test the accuracy of a hypothetic parameter value. Finally a confidence set can be created by finding the parameter values which can not be rejected. Bootstrapping the true residuals will be called abstract bootstrapping. We will show that the abstract bootstrap method is closely related to a permutation method. A balanced abstract bootstrap method will also be presented, a method which treats the grand mean in linear models and can be applied in ordinary bootstrapping as well. The resampling methods; bootstrap, abstract bootstrap and the permutation method are all closely related. Which method to use is discussed from a practical point of view.