On the layered nearest neighbour estimate, the bagged nearest neighbour estimate and the random forest method in regression and classification

Gérard Biau and Luc Devroye

Journal of Multivariate Analysis, 2010, vol. 101, issue 10, 2499-2518

Abstract: Let be identically distributed random vectors in , independently drawn according to some probability density. An observation is said to be a layered nearest neighbour (LNN) of a point if the hyperrectangle defined by and contains no other data points. We first establish consistency results on , the number of LNN of . Then, given a sample of independent identically distributed random vectors from , one may estimate the regression function by the LNN estimate , defined as an average over the Yi's corresponding to those which are LNN of . Under mild conditions on r, we establish the consistency of towards 0 as n-->[infinity], for almost all and all p>=1, and discuss the links between rn and the random forest estimates of Breiman (2001) [8]. We finally show the universal consistency of the bagged (bootstrap-aggregated) nearest neighbour method for regression and classification.

Keywords: Regression; estimation; Layered; nearest; neighbours; One; nearest; neighbour; estimate; Bagging; Random; forests (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (17)

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