An affine invariant k-nearest neighbor regression estimate

GéRard Biau,Luc Devroye,Vida Dujmović,Adam Krzyzak

Journal of Multivariate Analysis（2012）

引用 49|浏览9

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摘要

We design a data-dependent metric in R^d and use it to define the k-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard k-nearest neighbor regression estimate is asymptotically consistent under the usual conditions on k, and minimal requirements on the input data.

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关键词

usual condition,input data,regression estimate,minimal requirement,standard k-nearest neighbor regression,affine transformation,affine invariant k-nearest neighbor,k-nearest neighbor,estimation,random variables,k nearest neighbors,convergence,affine transformations,regression analysis,estimation theory,measurement

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