Abstract
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.
Citation
Hans-Georg Muller. "Adaptive Nonparametric Peak Estimation." Ann. Statist. 17 (3) 1053 - 1069, September, 1989. https://doi.org/10.1214/aos/1176347255
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