Kernel Density Estimation

Here K is the so-called kernel, i.e., a non-negative function that integrates to one and h is the so-called bandwidth of the kernel. Furthermore, the so-called scaled kernel Kh is defined as Kh(x) = 1 hK( x h). That is, Kh is obtained by stretching or shrinking, respectively, K regarding its width by the factor h, rescaling its height so that K again integrates up to one. A frequent choice for the kernel is the Gaussian kernel, i.e., K(y) = φ(y), where φ is the standard normal density function, i.e.,

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