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A weighted \(k\)-nearest neighbor density estimate for geometric inference. (English) Zbl 1274.62264

Summary: Motivated by a broad range of potential applications in topological and geometric inference, we introduce a weighted version of the \(k\)-nearest neighbor density estimate. Various pointwise consistency results of this estimate are established. We present a general central limit theorem under the lightest possible conditions. In addition, a strong approximation result is obtained and the choice of the optimal set of weights is discussed. In particular, the classical \(k\)-nearest neighbor estimate is not optimal in a sense described in the manuscript. The proposed method has been implemented to recover level sets in both simulated and real-life data.

MSC:

62G07 Density estimation
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference

Software:

ANN; CGAL
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Full Text: DOI Euclid

References:

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