ABSTRACT
This chapter discusses some methods other than the kernel method. Probably the only practical drawback of the kernel method of density estimation is its inability to deal satisfactorily with the tails of distributions without oversmoothing the main part of the density. The chapter introduces an extension of the variable kernel method, called the adaptive kernel method. A philosophical difficulty with the kernel method, and with most of the other methods for density estimation, is the rather ad hoc way in which the estimates are defined. The practical appeal of penalized likelihood in the specific context of density estimation is probably somewhat less than that of the other methods. The nearest neighbour method is widely used in the fields of pattern recognition and nonparametric discriminant analysis. Apart from the kernel method and the three methods discussed in the chapter, there are of course many other methods available for density estimation, such as the orthogonal series method.
