Optimal weighted nearest neighbour classifiers

@article{Samworth2012OptimalWN,
  title={Optimal weighted nearest neighbour classifiers},
  author={R. Samworth},
  journal={Annals of Statistics},
  year={2012},
  volume={40},
  pages={2733-2763}
}
  • R. Samworth
  • Published 2012
  • Mathematics
  • Annals of Statistics
We derive an asymptotic expansion for the excess risk (regret) of a weighted nearest-neighbour classifier. This allows us to find the asymptotically optimal vector of nonnegative weights, which has a rather simple form. We show that the ratio of the regret of this classifier to that of an unweighted k-nearest neighbour classifier depends asymptotically only on the dimension d of the feature vectors, and not on the underlying populations. The improvement is greatest when d=4, but thereafter… Expand

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