Definition:Kernel Density Estimation
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Definition
Kernel density estimation is a nonparametric method for estimating a probability density function of a continuous random variable $X$ based on data forming a (usually large) sample.
Kernel
The kernel of a probability density function of a continuous random variable $X$ is a probability function $\map k u$ symmetric about $u = 0$.
Bandwidth
Let there be $n$ data points of a probability density function $f$:
- $x_1, x_2, \ldots, x_n$
For each $x_i$ we can substitute:
- $u = \dfrac {x - x_i} h$
to make a function of $x$.
In this context, $h$ is referred to as the bandwidth of $f$.
Hence the estimated probabiity density function is given by:
- $\ds \map f x = \dfrac 1 {n h} \sum_{i \mathop = 1}^n \map k {\dfrac {x - x_i} h}$
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