Nearest Neighbor Smoother
The idea of the nearest neighbor smoother is the following. For each point X0, take m nearest neighbors and estimate the value of Y(X0) by averaging the values of these neighbors.
Formally, where is the mth closest to X0 neighbor, and
Example:
In this example, X is one-dimensional. For each X0, the is an average value of 16 closest to X0 points (denoted by red). The result is not smooth enough.
Read more about this topic: Kernel Smoother
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—Bible: Hebrew Psalm LV (l. LV, 21–22)