Asymptotic expansions of the \(k\) nearest neighbor risk

DOI10.1214/AOS/1024691080zbMath0929.62070OpenAlexW2035981651MaRDI QIDQ1807111

Robert R. Snapp, Santosh S. Venkatesh

Publication date: 9 November 1999

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1024691080

zbMATH Keywords

asymptotic expansionssimulationsLaplace's methodfinite-sample riskk-nearest neighbor classifier

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60)

Related Items (5)

Stein's identity, Fisher information, and projection pursuit: A triangulation ⋮ Choice of neighbor order in nearest-neighbor classification ⋮ Residual variance estimation using a nearest neighbor statistic ⋮ Theoretical analysis of cross-validation for estimating the risk of the k-Nearest Neighbor classifier ⋮ Nearest neighbor classification with dependent training sequences.

Cites Work

• Unnamed Item
• Consistent nonparametric regression. Discussion
• Asymptotics. II: Laplace's method for multiple integrals
• An Optimal Global Nearest Neighbor Metric
• Bias of Nearest Neighbor Error Estimates
• Any Discrimination Rule Can Have an Arbitrarily Bad Probability of Error for Finite Sample Size
• An Algorithm for Finding Best Matches in Logarithmic Expected Time
• On the finite sample performance of the nearest neighbor classifier
• Nearest neighbor pattern classification
• The Nearest Neighbor Classification Rule with a Reject Option

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