The Annals of Statistics

Weak Convergence and Adaptive Peak Estimation for Spectral Densities

Hans-Georg Muller and Kathryn Prewitt

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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.

Article information

Ann. Statist., Volume 20, Number 3 (1992), 1329-1349.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 62M15: Spectral analysis
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62G07: Density estimation 62G20: Asymptotic properties 62E20: Asymptotic distribution theory

Bandwidth choice cumulants curve estimation efficiency kernel estimators stationary process tightness time series variable bandwidth


Muller, Hans-Georg; Prewitt, Kathryn. Weak Convergence and Adaptive Peak Estimation for Spectral Densities. Ann. Statist. 20 (1992), no. 3, 1329--1349. doi:10.1214/aos/1176348771.

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