Definition:Kernel Density Estimation/Kernel

Definition

The kernel of a probability density function of a continuous random variable $X$ is a probability function $\map k u$ symmetric about $u = 0$.

There are several widely used choices used for such a kernel.

Gaussian Kernel

The Gaussian kernel of a probability density function is the kernel of the form:

$\map k u = \dfrac 1 {\sqrt {2 \pi} } e^{-u^2 / 2}$

Also see

• Results about kernel density estimation can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): kernel density estimation