ABSTRACT
This chapter discusses the main methods available for univariate density estimation. Many of the important applications of density estimation are to multivariate data, but since all the multivariate methods are generalizations of univariate methods, it is worth getting a feel for the univariate case first. When density estimates are needed as intermediate components of other methods, the case for using alternatives to histograms is quite strong. For the presentation and exploration of data, histograms are of course an extremely useful class of density estimates, particularly in the univariate case. The naive estimator is not wholly satisfactory from the point of view of using density estimates for presentation. The nearest neighbour class of estimators represents an attempt to adapt the amount of smoothing to the 'local' density of data. It is very often the case that the natural domain of definition of a density to be estimated is not the whole real line.
