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September, 1992 Weak Convergence and Adaptive Peak Estimation for Spectral Densities
Hans-Georg Muller, Kathryn Prewitt
Ann. Statist. 20(3): 1329-1349 (September, 1992). DOI: 10.1214/aos/1176348771


Adaptive nonparametric kernel estimators for the location of a peak of the spectral density of a stationary time series are proposed and investigated. They are based on direct smoothing of the periodogram where the amount of smoothing is determined automatically in an asymptotically optimal fashion. These adaptive estimators minimize the asymptotic mean squared error. Adaptivity is derived from the weak convergence of a two-parameter stochastic process in a deviation and a bandwidth coordinate to a Gaussian limit process. Efficient global and local bandwidth choices which lead to adaptive peak estimators and practical aspects are discussed.


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Hans-Georg Muller. Kathryn Prewitt. "Weak Convergence and Adaptive Peak Estimation for Spectral Densities." Ann. Statist. 20 (3) 1329 - 1349, September, 1992.


Published: September, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0781.62143
MathSciNet: MR1186252
Digital Object Identifier: 10.1214/aos/1176348771

Primary: 62M15
Secondary: 62E20, 62G07, 62G20, 62M10

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 3 • September, 1992
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