ABSTRACT
This chapter gives an overview of statistical smoothing, including the contexts of density estimation and nonparametric regression, also known as scatterplot smoothing. It is seen that the popular histogram for understanding one-dimensional distributions can be seriously hampered by the “bin edge effect”, which is elucidated using a kernel density estimator, suggesting the latter should be the natural default view (which is used throughout this book). The main ideas are illustrated by the Hidalgo Stamps and Bralower Fossils data sets. A brief discussion of data-based smoothing parameter selection is included. The utility of the SiZer (SIgnificance of ZERo Crossings) methodology for meaningful statistical inference is demonstrated with several real data sets, including the British Family Incomes data.
