Asymptotic Spectral Theory for Spatial Data

2020/05/27 by Wai Leong Ng, Ng, Wai Leong, Chun Yip Yau +1
Economics, Econometrics and Finance · Environmental Science · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Soil Geostatistics and Mapping #Statistics Theory (math.ST) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2005.13274

openalex publication_date 2020/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the asymptotic theory for spectral analysis of stationary random fields, 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.

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