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Tail estimation of the spectral density for a stationary Gaussian random field

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  • Wu, Wei-Ying
  • Lim, Chae Young
  • Xiao, Yimin

Abstract

Consider a stationary Gaussian random field on Rd with spectral density f(λ) that satisfies f(λ)∼c|λ|−θ as |λ|→∞. The parameters c and θ control the tail behavior of the spectral density. c is related to a microergodic parameter and θ is related to a fractal index. For data observed on a grid, we propose estimators of c and θ by minimizing an objective function, which can be viewed as a weighted local Whittle likelihood, study their properties under the fixed-domain asymptotics and provide simulation results.

Suggested Citation

  • Wu, Wei-Ying & Lim, Chae Young & Xiao, Yimin, 2013. "Tail estimation of the spectral density for a stationary Gaussian random field," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 74-91.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:74-91
    DOI: 10.1016/j.jmva.2012.11.014
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    References listed on IDEAS

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    Cited by:

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    2. Victor De Oliveira & Zifei Han, 2022. "On Information About Covariance Parameters in Gaussian Matérn Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 690-712, December.
    3. Chen, Kun & Chan, Ngai Hang & Yau, Chun Yip & Hu, Jie, 2023. "Penalized Whittle likelihood for spatial data," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    4. Claudio Durastanti, 2016. "Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 651-673, November.
    5. Girard, Didier A., 2016. "Asymptotic near-efficiency of the “Gibbs-energy and empirical-variance” estimating functions for fitting Matérn models — I: Densely sampled processes," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 191-197.

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