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|a (DE-627)JST008995982
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|a (JST)120060
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|a DE-627
|b ger
|c DE-627
|e rakwb
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|a eng
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|a Snapp, Robert R.
|e verfasserin
|4 aut
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|a Asymptotic Expansions of the k Nearest Neighbor Risk
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|c 1998
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|a Text
|b txt
|2 rdacontent
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|a The finite-sample risk of the k nearest neighbor classifier that uses a weighted Lp-metric as a measure of class similarity is examined. For a family of classification problems with smooth distributions in Rn, an asymptotic expansion for the risk is obtained in decreasing fractional powers of the reference sample size. An analysis of the leading expansion coefficients reveals that the optimal weighted Lp-metric, that is, the metric that minimizes the finite-sample risk, tends to a weighted Euclidean (i.e., L2) metric as the sample size is increased. Numerical simulations corroborate this finding for a pattern recognition problem with normal class-conditional densities.
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|a Copyright 1998 The Institute of Mathematical Statistics
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|a Primary 62G20, 62H30, 41A60
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|a k nearest neighbor classifier
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|a Finite-sample risk
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|a Asymptotic expansions
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|a Laplace's method
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|a Mathematics
|x Pure mathematics
|x Discrete mathematics
|x Number theory
|x Numbers
|x Real numbers
|x Rational numbers
|x Integers
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Measures of variability
|x Sample size
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Vector analysis
|x Mathematical vectors
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|a Social sciences
|x Human geography
|x Social geography
|x Neighborhoods
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|a Philosophy
|x Metaphysics
|x Etiology
|x Determinism
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|a Physical sciences
|x Physics
|x Mechanics
|x Density
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|a Mathematics
|x Pure mathematics
|x Linear algebra
|x Linear transformations
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|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Cognitive processes
|x Pattern recognition
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|a Philosophy
|x Logic
|x Logical topics
|x Formal logic
|x Mathematical logic
|x Mathematical set theory
|x Lattice theory
|x Mathematical lattices
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|a Mathematics
|x Pure mathematics
|x Calculus
|x Differential calculus
|x Mathematical integration
|x Laplaces method
|x Classification
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|a research-article
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|a Venkatesh, Santosh S.
|e verfasserin
|4 aut
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|i Enthalten in
|t The Annals of Statistics
|d Institute of Mathematical Statistics
|g 26(1998), 3, Seite 850-878
|w (DE-627)270129162
|w (DE-600)1476670-X
|x 00905364
|7 nnns
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|g volume:26
|g year:1998
|g number:3
|g pages:850-878
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|u https://www.jstor.org/stable/120060
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|a AR
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|d 26
|j 1998
|e 3
|h 850-878
|