Spectral analysis for harmonizable processes. (English) Zbl 1012.62099

Lii, Keh-Shin; Rosenblatt, Murray

Ann. Stat. 30, No. 1, 258-297 (2002).

Summary: 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.

MSC:

62M15	Inference from stochastic processes and spectral analysis
60G20	Generalized stochastic processes
62F12	Asymptotic properties of parametric estimators
62G07	Density estimation

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[26]	UNIVERSITY OF CALIFORNIA, RIVERSIDE RIVERSIDE, CALIFORNIA 92521 E-MAIL: [e-mail] DEPARTMENT OF MATHEMATICS UNIVERSITY OF CALIFORNIA, SAN DIEGO LA JOLLA, CALIFORNIA 92093 E-MAIL: [e-mail]