Bootstrap confidence intervals in nonparametric regression without an additive model

Abstract

The problem of confidence interval construction in nonparametric regression via the bootstrap is revisited. When an additive model holds true, the usual residual bootstrap is available but it often leads to confidence interval under-coverage

the case is made that this under-coverage can be partially corrected using predictive—as opposed to fitted—residuals for resampling. Furthermore, it has been unclear to date if a bootstrap approach is feasible in the absence of an additive model. The main thrust of this paper is to show how the transformation approach put forth by Politis (Test 22(2):183–221, 2013) in the related setting of prediction intervals can be found useful in order to construct bootstrap confidence intervals without an additive model. © Springer Science+Business Media New York 2014.