When the number of features p is large, there tends to be a deteri

oration in the performance of KNN and other local approaches that

perform prediction using only observations that are near the test ob

servation for which a prediction must be made. This phenomenon is

known as the curse of dimensionality, and it ties into the fact that curse of di

non$-$parametric approaches often perform poorly when p is large. We

will now investigate this curse.