Weak convergence of \(k\)-NN density and regression estimators with varying \(k\) and applications

DOI10.1214/aos/1176350487zbMath0643.62027OpenAlexW2002225341MaRDI QIDQ1102052

P. K. Bhattacharya, Y. P. Mack

Publication date: 1987

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1176350487

zbMATH Keywords

weak convergenceorder statisticsdensity estimationBLUEregression estimationinduced order statisticscontinuous time stochastic processesuniform weightsasymptotic linear modelsbiased linear combinations of k-NN estimatorsk-nearest neighbor estimatorssecond- order smoothness conditionsuniform kernel

Mathematics Subject Classification ID

Nonparametric estimation (62G05) Order statistics; empirical distribution functions (62G30) General nonlinear regression (62J02) Functional limit theorems; invariance principles (60F17)

Related Items (13)

k-NEAREST NEIGHBOR ESTIMATION OF INVERSE-DENSITY-WEIGHTED EXPECTATIONS WITH DEPENDENT DATA ⋮ A note on the asymptotic behavior of conditional extremes ⋮ Asymptotic properties for median cross-validated nearest neighbor median estimate in nonparametric regression ⋮ The \(k\)-nearest neighbors method in single index regression model for functional quasi-associated time series data ⋮ A weighted \(k\)-nearest neighbor density estimate for geometric inference ⋮ Functionals of order statistics and their multivariate concomitants with application to semiparametric estimation by nearest neighbours ⋮ On the Hilbert kernel density estimate ⋮ Stochastic approximation and selection of a conditional extermal function in continuum ⋮ Location-adaptive density estimation and nearest-neighbor distance ⋮ Convergence of \(k\) nearest neighbor kernel estimator in nonparametric functional regression ⋮ BIAS-CORRECTED CONFIDENCE INTERVALS FOR WILDLIFE ABUNDANCE ESTIMATION ⋮ Multivariate data-driven k-NN function estimation ⋮ Nearest neighbor forecasting using sparse data representation

This page was built for publication: Weak convergence of \(k\)-NN density and regression estimators with varying \(k\) and applications