The uniform convergence of nearest neighbor regression function estimators and their application in optimization

Authors:
L. Devroye
Affiliations:
-
Venue:
IEEE Transactions on Information Theory
Year:
2006

Citing 0
Cited 4

Scheduling in a dynamic heterogeneous distributed system using estimation error

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

Journal of Multivariate Analysis
Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments

Computational Statistics & Data Analysis
Limit Theorems for Simulation-Based Optimization via Random Search

ACM Transactions on Modeling and Computer Simulation (TOMACS)

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Abstract

A class of nonparametric regression function estimates generalizing the nearest neighbor estimate of Cover [ 12] is presented. Under various noise conditions, it is shown that the estimates are strongly uniformly consistent. The uniform convergence of the estimates can be exploited to design a simple random search algorithm for the global minimization of the regression function.