An optimal k-nearest neighbor for density estimation
AbstractA 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 82 (2012)
Issue (Month): 10 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- 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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