Definitions
Let be a kernel defined by
where:
- is the Euclidean norm
- is a parameter (kernel radius)
- D(t) typically is a positive real valued function, which value is decreasing (or not increasing) for the increasing distance between the X and X0.
Popular kernels used for smoothing include
- Epanechnikov
- Tri-cube
- Gaussian
Let be a continuous function of X. For each, the Nadaraya-Watson kernel-weighted average (smooth Y(X) estimation) is defined by
where:
- N is the number of observed points
- Y(Xi) are the observations at Xi points.
In the following sections, we describe some particular cases of kernel smoothers.
Read more about this topic: Kernel Smoother
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