Kernel Smoother - Nearest Neighbor Smoother

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

D(t)= \begin{cases} 1/m & \text{if } |t| \le 1 \\ 0 & \text{otherwise} \end{cases}

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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