Nearest-Neighbor Methods

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Nearest-neighbor methods use those observations in the training set T closest in input space to x  form Y-hat.

Specifically, the k-nearest neighbor fit for Y-hat is difined as follows: Y(x)=1/kΣyi,xi belong to Nk(x).

where Nk(x) is the neighborhood of x defined by the k closest points xi in the traing sample.

Closeness implies a metric, which for the moment we assume is Euclidean distance. So, in words, we find the k observations with xi closest to x in input space, and average their responses.

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