Optimal choice of k for k-nearest neighbor regression

09/12/2019

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by   Mona Azadkia, et al.

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The k-nearest neighbor algorithm (k-NN) is a widely used non-parametric method for classification and regression. We study the mean squared error of the k-NN estimator when k is chosen by leave-one-out cross-validation (LOOCV). Although it was known that this choice of k is asymptotically consistent, it was not known previously that it is an optimal k. We show, with high probability, the mean squared error of this estimator is close to the minimum mean squared error using the k-NN estimate, where the minimum is over all choices of k.