ESL, p. 42 says:
Hence most data points are closer to the boundary of the sample space than to any other data point. The reason that this presents a problem is that prediction is much more difficult near the edges of the training sample. One must extrapolate from neighboring sample points rather than interpolate between them.
I understand that extrapolation is harder than interpolation. And I understand that if we choose a point to predict and it happens to be near the edge of the sample space, we are more likely to have to extrapolate.
But a large part of the training data set is also near the edge. And the more training points nearby, the better chance we have to interpolate instead of extrapolate. Doesn't the fact that many training points are near the edge reduce or even eliminate the problem that many points we want to predict for are near the edge?