Rates of Convergence for the Normal and the Bootstrap Approximations in Nonparametric Regression

This paper is concerned with the distributions used to construct confidence intervals for the regression function in a nonparametric setup. The rates of convergence for the normal limit, its plug in approach and the wild bootstrap are compared conditionally on the explanatory variable X and also unconditionally. It turns out that the wild bootstrap performs better than the other approximations conditionally, but this behavior does not hold in the unconditional situation.