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An optimal k-nearest neighbor for density estimation


  • Kung, Yi-Hung
  • Lin, Pei-Sheng
  • Kao, Cheng-Hsiung


A k-nearest neighbor method, which has been widely applied in machine learning, is a useful tool to obtain statistical inference for an underlying distribution of multi-dimensional data. However, the knowledge on choosing an optimal order for the k-nearest neighbor is relatively little. This paper proposes an asymptotic distribution for the nearest neighbor statistic. Under some conditions, we find an optimal unbiased density estimate based on a linear combination of nearest neighbors, and it leads to an optimal choice for the order of the k-nearest neighbor.

Suggested Citation

  • Kung, Yi-Hung & Lin, Pei-Sheng & Kao, Cheng-Hsiung, 2012. "An optimal k-nearest neighbor for density estimation," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1786-1791.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:10:p:1786-1791
    DOI: 10.1016/j.spl.2012.05.017

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    References listed on IDEAS

    1. Mack, Y. P. & Rosenblatt, M., 1979. "Multivariate k-nearest neighbor density estimates," Journal of Multivariate Analysis, Elsevier, vol. 9(1), pages 1-15, March.
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