期刊
STATISTICS & PROBABILITY LETTERS
卷 82, 期 10, 页码 1786-1791出版社
ELSEVIER
DOI: 10.1016/j.spl.2012.05.017
关键词
Density estimation; Multi-dimensional data; Nearest neighbor method
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. (C) 2012 Elsevier B.V. All rights reserved.
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