In the context of a heteroscedastic nonparametric regression model, we develop a test for the null hypothesis that a subset of the predictors has no influence on the regression function. The test uses residuals obtained from local polynomial fitting of the null model and is based on a test...

In this article, we propose a new method of bias reduction in nonparametric regression estimation. The proposed new estimator has asymptotic bias order h4, where h is a smoothing parameter, in contrast to the usual bias order h2 for the local linear regression. In addition, the proposed...