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September, 1987 Weak Convergence of $k$-NN Density and Regression Estimators with Varying $k$ and Applications
P. K. Bhattacharya, Y. P. Mack
Ann. Statist. 15(3): 976-994 (September, 1987). DOI: 10.1214/aos/1176350487

Abstract

In both density and regression estimation problems, the $k$-nearest neighbor estimators with $k$ varying in an appropriate range, when transformed to continuous time stochastic processes, are shown to have a common limiting structure under the usual second-order smoothness conditions as the sample size tends to $\infty$. These results lead to asymptotic linear models in which BLUE's and suitably biased linear combinations are considered.

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P. K. Bhattacharya. Y. P. Mack. "Weak Convergence of $k$-NN Density and Regression Estimators with Varying $k$ and Applications." Ann. Statist. 15 (3) 976 - 994, September, 1987. https://doi.org/10.1214/aos/1176350487

Information

Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0643.62027
MathSciNet: MR902240
Digital Object Identifier: 10.1214/aos/1176350487

Subjects:
Primary: 62G05
Secondary: 60F17, 62G20, 62G30, 62J02

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • September, 1987
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