Asymptotic spectral theory for spatial data. Issue 3 (3rd April 2023)

• Record Type: Journal Article
• Authors: Ng, Wai Leong; Yau, Chun Yip
• Is Part Of: Stochastics. Volume 95:Issue 3(2023)
• Page Start: 423
• Page End: 464
• Publication Date: 2023-04-03
• Subjects: Fourier coefficients -- geometric moment contraction -- periodograms -- spectral analysis -- spectral density estimation; 62M15 -- 62E20 -- 62M30; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2022.2086806
• Languages: English
• ISSNs: 1744-2508

Abstract

ABSTRACT: In this paper, we study the asymptotic theory for spectral analysis of stationary random fields on Z 2, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of Fourier coefficients, and the uniform consistency of kernel spectral density estimators are obtained under various mild conditions on moments and dependence structures. The validity of the aforementioned asymptotic results for estimated spatial fields is also established.