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Weak Convergence of k-NN Density and Regression Estimators with Varying k and Applications

P. K. Bhattacharya and Y. P. Mack
The Annals of Statistics
Vol. 15, No. 3 (Sep., 1987), pp. 976-994
Stable URL: http://www.jstor.org/stable/2241810
Page Count: 19
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Weak Convergence of k-NN Density and Regression Estimators with Varying k and Applications
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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 ∞. These results lead to asymptotic linear models in which BLUE's and suitably biased linear combinations are considered.

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