Corpus ID: 222090989

Analysis of KNN Density Estimation

@article{Zhao2020AnalysisOK,
  title={Analysis of KNN Density Estimation},
  author={Puning Zhao and Lifeng Lai},
  journal={ArXiv},
  year={2020},
  volume={abs/2010.00438}
}
We analyze the $\ell_1$ and $\ell_\infty$ convergence rates of k nearest neighbor density estimation method. Our analysis includes two different cases depending on whether the support set is bounded or not. In the first case, the probability density function has a bounded support and is bounded away from zero. We show that kNN density estimation is minimax optimal under both $\ell_1$ and $\ell_\infty$ criteria, if the support set is known. If the support set is unknown, then the convergence… Expand

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