ABSTRACT
This chapter proposes data-driven procedures for selecting a constant or variable bandwidth in local polynomial fitting. The basic ingredients for the procedures are simple. As a by-product of the estimated bias and variance, the chapter discusses the construction of pointwise confidence intervals. The chapter introduces a second basic ingredient is a residual squares criterion. It discusses briefly the property of spatial adaptation and its importance in nonparametric regression. The chapter outlines the key idea of the local modelling scheme in likelihood-based models, and shows how the bandwidth can be chosen automatically by using the data. It discusses the cross-validation technique, the normal-reference method, the plug-in approach, and the bandwidth selection rule proposed by S. J. Sheather and M. C. Jones. The chapter discusses an adaptive bandwidth selector which is very simple in nature and is therefore quite appealing to use when the design points are not uniform.
