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February 2002 Spectral analysis for harmonizable processes
Keh-Shin Lii, Murray Rosenblatt
Ann. Statist. 30(1): 258-297 (February 2002). DOI: 10.1214/aos/1015362193


Spectral estimation of nonstationary but harmonizable processes is considered. Given a single realization of the process, periodogram-like and consistent estimators are proposed for spectral mass estimation when the spectral support of the process consists of lines. Such a process can arise in signals of a moving source from array data or multipath signals with Doppler stretch from a single receiver. Such processes also include periodically correlated (or cyclostationary) and almost periodically correlated processes as special cases. We give detailed analysis on aliasing, bias and covariances of various estimators. It is shown that dividing a single long realization of the process into nonoverlapping subsections and then averaging periodogram-like estimates formed from each subsection will not yield meaningful results if one is estimating spectral mass with support on lines with slope not equal to 1. If the slope of a spectral support line is irrational, then spectral masses do not fold on top of each other in estimation even if the data are equally spaced. Simulation examples are given to illustrate various theoretical results.


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Keh-Shin Lii. Murray Rosenblatt. "Spectral analysis for harmonizable processes." Ann. Statist. 30 (1) 258 - 297, February 2002.


Published: February 2002
First available in Project Euclid: 6 March 2002

zbMATH: 1012.62099
MathSciNet: MR1892664
Digital Object Identifier: 10.1214/aos/1015362193

Primary: 62M15
Secondary: 60G12 , 62F12 , 62G07

Keywords: Aliasing , bias , consistency , Covariance , cyclostationary , Doppler , estimation , harmonizable processes , multipath , spectral density function

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.30 • No. 1 • February 2002
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