Better Bootstrap Confidence Intervals for Regression Curve Estimation

Abstract

Bootstrap methods in curve estimation have been introduced for smoothing parameter selection and for construction of confidence intervals. Most of the papers on confidence intervals use explicit bias estimation or the technique of "undersmoothing" to deal with bias. Coverage accuracy has only been considered for curve estimates with constant variance function. In this paper we show that explicit bias estimation even with heteroscedastic variance structure leads to an improvement of coverage accuracy, when compared to undersmoothing. Bootstrapping with this bias correction using the so-called wild bootstrap leads to an improved coverage accuracy.

Keywords:

• AMS 1991 subject classifications
• Primary 62G07
• secondary 62G09

Keywords:

• Bootstrap
• nonparametric regression
• wild bootstrap
• kernel estimators