ABSTRACT

The survey is not intended to be exhaustive or prescriptive, but it is hoped that it will emphasize the applicability of density estimation to a variety of topics. With this aim in mind, this chapter focuses on methods that are based fairly explicitly on density estimation ideas, without necessarily claiming that these are the only or even the best approaches. The chapter discusses the application of density estimation to statistical discrimination. Several authors have conducted simulation studies to investigate the density estimation approach to nonparametric discriminant analysis, and to compare it with classical approaches. An interesting possibility in nonparametric discrimination using density estimates is the definition of an atypicality index for observations assigned to a particular population. The choice of smoothing parameter in the smoothed bootstrap is usually made completely arbitrarily; detailed work on this choice, making use of known properties of density estimates, would no doubt improve the performance of the smoothed bootstrap.