Bootstrap and wild bootstrap for high — dimensional linear random design models

Abstract

In this chapter two bootstrap procedures are studied for high - dimensional linear models where the design vectors are random and the dimension p of the parameter is large. The stochastic structure of this model is more complex than in the case of linear models with nonrandom design which have been considered in the last two chapters. There the bootstrap procedure has to mimic the relatively simple case of one dimensional i. i. d. error variables. Now the model will be described by distributions in high dimensional spaces. We will see that bootstrap works in this more complex model not always as satisfactorily as in the case of a nonrandom design.