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September, 1989 Adaptive Nonparametric Peak Estimation
Hans-Georg Muller
Ann. Statist. 17(3): 1053-1069 (September, 1989). DOI: 10.1214/aos/1176347255


It is shown that consistent estimates of the optimal bandwidths for kernel estimators of location and size of a peak of a regression function are available. Such estimates yield the same joint asymptotic distribution of location and size of a peak as the optimal bandwidths themselves. Therefore data-adaptive efficient estimation of peaks is possible. In order to prove this result, the weak convergence of a two-dimensional stochastic process with appropriately scaled bandwidths as arguments to a Gaussian limiting process is shown. A practical method which leads to consistent estimates of the optimal bandwidths and is therefore asymptotically efficient is proposed and its finite sample properties are investigated by simulation.


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Hans-Georg Muller. "Adaptive Nonparametric Peak Estimation." Ann. Statist. 17 (3) 1053 - 1069, September, 1989.


Published: September, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0683.62019
MathSciNet: MR1015137
Digital Object Identifier: 10.1214/aos/1176347255

Primary: 62G05
Secondary: 62G20

Rights: Copyright © 1989 Institute of Mathematical Statistics


Vol.17 • No. 3 • September, 1989
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