Bootstrap, Wild Bootstrap and Generalized Bootstrap

Some modifications and generalizations of the bootstrap procedurehave been proposed. In this note we will consider the wild bootstrap and the generalized bootstrap and we will give two arguments why it makes sense touse these modifications instead of the original bootstrap. The firstargument is that there exist examples where generalized and wild bootstrapwork, but where the original bootstrap fails and breaks down. The secondargument will be based on higher order considerations. We will show thatthe class of generalized and wild bootstrap procedures offers a broadspectrum of possibilities for adjusting higher order properties of the bootstrap