The Annals of Statistics

Weak Convergence and Adaptive Peak Estimation for Spectral Densities

Hans-Georg Muller and Kathryn Prewitt

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348771

Digital Object Identifier
doi:10.1214/aos/1176348771

Mathematical Reviews number (MathSciNet)
MR1186252

Zentralblatt MATH identifier
0781.62143

JSTOR
links.jstor.org

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.aos/1176348771


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