Tie the straps: Uniform bootstrap confidence bands for semiparametric additive models

Abstract

This study considers the theoretical bootstrap “coupling” techniques for nonparametric robust smoothers and quantile regression, and we verify the bootstrap improvement. To handle the curse of dimensionality, a variant of “coupling” bootstrap techniques is developed for additive models both in a robust mean regression and in a quantile regression framework. Our bootstrap method can be used in many situations such as constructing confidence intervals and bands. We demonstrate the bootstrap improvement over the theoretical asymptotic band in simulations and in applications to firm expenditures and the interaction of economic sectors and the stock market.