Tie the straps

We consider theoretical bootstrap "coupling" techniques for nonparametric robust smoothers and quantile regression, and verify the bootstrap improvement. To cope with curse of dimensionality, a variant of "coupling" bootstrap techniques are developed for additive models with both symmetric error distributions and further extension to the quantile regression framework. Our bootstrap method can be used in many situations like constructing confidence intervals and bands. We demonstrate the bootstrap improvement over the asymptotic band theoretically, and also in simulations and in applications to firm expenditures and the interaction of economic sectors and the stock market.