Nonparametric Density Estimation
This chapter presents a background material, describing the fundamental concepts related to the nonparametric density estimation. First, a well-known histogram technique is briefly presented together with a description of its main drawbacks. To avoid the highlighted problems, at least to some extent, one might use a smart histogram modification known in the literature as an averaged shifted histogram (ASH). A simple example presented in this chapter shows its advantages over the classical histogram. The subsequent part of the chapter gives a general formulation of nonparametric density estimation, followed by the presentation of two basic approaches (the Parzen windows and the k-nearest neighbors (KNN)). Finally, the main advantages and drawbacks of the presented methods are described. The chapter is richly illustrated with a number of numerical examples.