Kernel Average Smoother
The idea of the kernel average smoother is the following. For each data point X0, choose a constant distance size λ (kernel radius, or window width for p = 1 dimension), and compute a weighted average for all data points that are closer than to X0 (the closer to X0 points get higher weights).
Formally, and D(t) is one of the popular kernels.
Example:
For each X0 the window width is constant, and the weight of each point in the window is schematically denoted by the yellow figure in the graph. It can be seen that the estimation is smooth, but the boundary points are biased. The reason for that is the non-equal number of points (from the right and from the left to the X0) in the window, when the X0 is close enough to the boundary.
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