ABSTRACT
This chapter focuses on some of the computational aspects of density estimation and smoothing algorithms. It deals with some of the basic concepts from density estimation, and examines some recent developments in smoothing. Smoothing can help to reveal structure against a background of randomness; it can also disguise the fact that there is little structure other than randomness. The histogram is the first, simplest, and most familiar example of a density estimator. It is a good context in which to fix some of the important ideas and to raise some important computational issues. From a practical standpoint, the naive estimate is somewhat better than the histogram, in that the notion of nearness that it embodies is more sensible. Generally kernels are both positive and symmetric about zero, but it is occasionally useful to relax these conditions. Despite the superficial similarities between the histogram estimator and the naive uniform kernel estimator, they are quite different computationally.
