Necessary and sufficient condition for the existence of a limit distribution of the nearest-neighbour density estimator

DOI10.1080/10485252.2011.567334zbMath1284.62248OpenAlexW2061591699MaRDI QIDQ3106415

Rémi Servien, Alain F. Berlinet

Publication date: 21 December 2011

Published in: Journal of Nonparametric Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10485252.2011.567334

zbMATH Keywords

asymptotic normalityregularity indexsmall ball probabilitynearest-neighbour estimator

Mathematics Subject Classification ID

Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Probability distributions: general theory (60E05)

Related Items

\(k\)NN estimation in functional partial linear modeling ⋮ Precise small deviations in \(L_2\) of some Gaussian processes appearing in the regression context ⋮ Unnamed Item

Cites Work

• Higher order estimation at Lebesgue points
• The strong uniform consistency of nearest neighbor density estimates
• Discriminatory Analysis. Nonparametric Discrimination: Consistency Properties
• Optimization of k nearest neighbor density estimates
• A Nonparametric Estimate of a Multivariate Density Function

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