Smooth Residual Bootstrap for Empirical Processes of Non‐parametric Regression Residuals

Abstract

Abstract. The aim of this paper is to prove the validity of smooth residual bootstrap versions of procedures that are based on the empirical process of residuals estimated from a non‐parametric regression model. From this result, consistency of various model tests in non‐parametric regression is deduced, such as goodness‐of‐fit tests for the regression and variance function, tests for equality of regression functions and tests concerning the error distribution.