Local Properties of k-NN Regression Estimates

DOI10.1137/0602035zbMath0499.62037OpenAlexW1998050127MaRDI QIDQ3965414

Y. P. Mack

Publication date: 1981

Published in: SIAM Journal on Algebraic Discrete Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0602035

zbMATH Keywords

asymptotic normalityrates of convergencevariancebiasregression estimatesk-nearest neighbor estimator

Mathematics Subject Classification ID

Nonparametric estimation (62G05) General nonlinear regression (62J02)

Related Items

Estimation of the optimal design of a nonlinear parametric regression problem via Monte Carlo experiments, Some asymptotic properties of nonparametric regression estimators in case of randomly censored data, A note on strong convergence rates in nonparametric regression, Adaptive nonparametric estimation of a multivariate regression function, Strong uniform consistency of nonparametric regression function estimates, A note on the asymptotic behaviour of the distance of the k_nth nearest neighbour, Optimal Nonparametric Inference with Two-Scale Distributional Nearest Neighbors, Large Scale Prediction with Decision Trees, The \(k\)-nearest neighbors method in single index regression model for functional quasi-associated time series data, Nonparametric estimation of non-stationary velocity fields from 3D particle tracking velocimetry data, Consistent nonparametric multiple regression for dependent heterogeneous processes: the fixed design case, Asymptotic behavior of encompassing test for independent processes: Case of linear and nearest neighbor regressions, Stochastic temporal data upscaling using the generalized \(k\)-nearest neighbor algorithm, Convergence of \(k\) nearest neighbor kernel estimator in nonparametric functional regression, Nonparametric estimation of conditional expectation, On the almost everywhere properties of the kernel regression estimate, Nonparametric estimation of a latent variable model, Smoothing spline regression estimation based on real and artificial data, Doubly robust multiple imputation using kernel-based techniques, k-Nearest Neighbour method in functional nonparametric regression, On conditional distributions of nearest neighbors, Robust nonparametric regression estimation, Multivariate data-driven k-NN function estimation, Strong laws of large numbers for arrays of row-wise extended negatively dependent random variables with applications, Symmetrized Multivariatek-NN Estimators, Nearest neighbor regression estimation for null-recurrent Markov time series, Nonparametric Knn estimation with monotone constraints, Estimation of a regression function corresponding to latent~variables, Weak and strong uniform consistency of kernel regression estimates

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Consistent nonparametric regression. Discussion
• The strong uniform consistency of nearest neighbor density estimates
• Estimation of a regression function by the parzen kernel-type density estimators
• Multivariate k-nearest neighbor density estimates
• Nonparametric estimates of probability densities
• Variable Kernel Estimates of Multivariate Densities
• Probability Inequalities for Sums of Bounded Random Variables