Abstract
We discuss anew the kernel method, which is representative of approaches to nonparametric scatter plot smoothing. This paper proposes a new estimator obtained by adding an adjustment term to an initial estimator, where the initial estimator is the well known local polynomial estimator. An appealing feature of the proposed estimator is that it reduces bias; the effect can be observed especially when the true regression function has large curvature. In this paper, we emphasize practical aspects of the use of our proposal, such as introducing a reliable bandwidth selection method and its evaluation, constructing a pointwise approximate confidence interval for the true regression function based on asymptotic normality of the estimator, and comparing our proposal with existing estimators by conducting a large size simulation study.
