Optimal rates for k-NN density and mode estimation

Part of Advances in Neural Information Processing Systems 27 (NIPS 2014)

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Sanjoy Dasgupta, Samory Kpotufe


We present two related contributions of independent interest: (1) high-probability finite sample rates for $k$-NN density estimation, and (2) practical mode estimators -- based on $k$-NN -- which attain minimax-optimal rates under surprisingly general distributional conditions.