Parzen-Window

Resources: page=190

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A method for Density Estimation which involves assuming that the region ${\mathcal{R}}_n$ is a $d$-dimension hypercube. We want to find out how many samples that end up in the hypercube ($k_n$).

$$k_n=\sum _{i=1}^n\varphi \left(\frac{x-x_i}{h_n}\right)$$

Where

• $h_n$ is the length of an edge of the hypercube
• $\varphi (u)=\{\begin{array}{ll}1& |u_j|\le \frac{1}{2},j=1,\dots ,d\\ 0& \text{otherwise}\end{array}$ is the window function