In kernel estimator, we have to choose h parameter as a bandwidth of the kernel, I know that there are methods to choose the parameter h. Also, there are two extreme cases on choosing h, if we choose h to tend to zero this will lead to the nearest neighbor estimator, and the opposite if we choose h to tend to infinity the will lead to the naive estimator. My question is what is the theoretical justification of these two extremes and what is the reference(book/journal)?
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Welcome to StackOverflow! Please, provide concrete examples. Someone will be likely to answer faster that way. – Arian Acosta Mar 07 '18 at 19:41
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I do not have an example but what I mean that if h is very small (close to zero) the kernel will put large weights on the neighbors of the point x (under estimate) and less weight on the rest of points, so this will be the nearest neighbour estimator. While if h is very large, the kernel will put equal weight on all points to estimate point x, and this will be the naive estimator. – faa Mar 07 '18 at 20:34