BOOTSTRAP AND WILD BOOTSTRAP FOR HIGH-DIMENSIONAL LINEAR-MODELS

In this paper two bootstrap procedures are considered for the estimati on of the distribution of linear contrasts and of F-test statistics in high dimensional linear models. An asymptotic approach will be chosen where the dimension p of the model may increase for sample size n --> infinity. The range of validity will be compared for the normal appro ximation and for the bootstrap procedures. Furthermore, it will be arg ued that the rates of convergence are different for the bootstrap proc edures in this asymptotic framework. This is in contrast to the usual asymptotic approach where p is fixed.