The Annals of Statistics

Estimation for almost periodic processes

Keh-Shin Lii and Murray Rosenblatt

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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.

Article information

Ann. Statist., Volume 34, Number 3 (2006), 1115-1139.

First available in Project Euclid: 10 July 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M15: Spectral analysis 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G05: Estimation 62M99: None of the above, but in this section

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


Lii, Keh-Shin; Rosenblatt, Murray. Estimation for almost periodic processes. Ann. Statist. 34 (2006), no. 3, 1115--1139. doi:10.1214/009053606000000218.

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