Pattern Recognition, 4th Edition

2.5.6. Nonparametric Estimation

So far in our discussion a pdf parametric modeling has been incorporated, in one way or another, and the associated unknown parameters have been estimated. In the current subsection we will deal with nonparametric techniques. These are basically variations of the histogram approximation of an unknown pdf, which is familiar to us from our statistics basics. Let us take, for example, the simple one-dimensional case. Figure 2.18 shows two examples of a pdf and its approximation by the histogram method. That is, the x-axis (one-dimensional space) is first divided into successive bins of length h. Then the probability of a sample x being located in a bin is estimated for each of the bins. If N is the total number ...