ABSTRACT
The selection of the bandwidth is the single most crucial factor in determining the performance of a kernel estimator. This chapter examines the different bandwidth selectors in more detail. Normal scale bandwidths are often the first selectors to be developed for a kernel estimator as they are the simplest in terms of mathematical and computational complexity. Plug-in bandwidth selectors were first introduced for multivariate data for constrained matrices by Wand and Jones, who extended the univariate methodology of Sheather and Jones. A third main flavour of cross validation, known as smoothed cross validation (SCV), has shown more promise than biased cross validation in the goal to reduce the large variability of unbiased cross validation. This is achieved by an improved estimator of the integrated squared bias. The chapter provides more details about the behaviour of kernel estimators: whilst they are not required for practical data analysis, they contribute to a deeper understanding and appreciation of their important properties.
