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June 2006 Estimation for almost periodic processes
Keh-Shin Lii, Murray Rosenblatt
Ann. Statist. 34(3): 1115-1139 (June 2006). DOI: 10.1214/009053606000000218

Abstract

Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration if the locations of the lines are known. Here methods for estimating the intercepts of the lines of spectral concentration in the Gaussian case are given under appropriate conditions. The methods determine rates of convergence sufficiently fast as the sample size n→∞ so that the spectral estimation on the estimated lines can then proceed effectively. This task involves bounding the maximum of an interesting class of non-Gaussian possibly nonstationary processes.

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Keh-Shin Lii. Murray Rosenblatt. "Estimation for almost periodic processes." Ann. Statist. 34 (3) 1115 - 1139, June 2006. https://doi.org/10.1214/009053606000000218

Information

Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1113.62111
MathSciNet: MR2278353
Digital Object Identifier: 10.1214/009053606000000218

Subjects:
Primary: 62M10 , 62M15
Secondary: 62G05 , 62M99

Keywords: Almost periodic covariance , frequency detection and estimation , Gaussian and non-Gaussian process , periodogram , process maximum , spectral estimation

Rights: Copyright © 2006 Institute of Mathematical Statistics

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Vol.34 • No. 3 • June 2006
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