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Statistical analysis of irregularly spaced spatial data in frequency domain

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  • Shibin Zhang

Abstract

Central limit theorems (CLTs) for frequency‐domain statistics are fundamental tools in frequency‐domain analysis. However, for irregularly spaced data, they are still limited. In both the pure increasing domain and the mixed increasing domain asymptotic frameworks, three CLTs of frequency‐domain statistics are established for the observations at uniformly distributed sampling locations over a rectangular sampling region. One is for discrete Fourier transforms (DFTs), while the other two pertain to generalized spectral means (GSMs). The asymptotic joint normality and independence of the DFT at any finite number of standard frequencies are derived. Additionally, the asymptotic normalities of two GSMs are set up, with asymptotic variances given in different forms, according to the Gaussian or non‐Gaussian model assumption. Three established CLTs are very useful in investigating the sampling properties of many important frequency‐domain statistics, such as periodogram, non‐negative definite auto‐covariance estimator, spectral density estimator, and Whittle likelihood estimator as well.

Suggested Citation

  • Shibin Zhang, 2024. "Statistical analysis of irregularly spaced spatial data in frequency domain," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(5), pages 714-738, September.
    • Handle: RePEc:bla:jtsera:v:45:y:2024:i:5:p:714-738
    DOI: 10.1111/jtsa.12735
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    References listed on IDEAS

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    1. Soutir Bandyopadhyay & Suhasini Subba Rao, 2017. "A test for stationarity for irregularly spaced spatial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 95-123, January.
    2. Haihan Yu & Mark S Kaiser & Daniel J Nordman, 2023. "A subsampling perspective for extending the validity of state-of-the-art bootstraps in the frequency domain," Biometrika, Biometrika Trust, vol. 110(4), pages 1099-1115.
    3. Shibin Zhang, 2023. "A copula spectral test for pairwise time reversibility," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 705-729, October.
    4. Fuentes, Montserrat, 2007. "Approximate Likelihood for Large Irregularly Spaced Spatial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 321-331, March.
    5. Moreno Bevilacqua & Carlo Gaetan & Jorge Mateu & Emilio Porcu, 2012. "Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 268-280, March.
    6. Yasumasa Matsuda & Yoshihiro Yajima, 2009. "Fourier analysis of irregularly spaced data on Rd," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 191-217, January.
    7. Michael L. Stein, 2005. "Statistical methods for regular monitoring data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 667-687, November.
    8. Jie Chen & Michael L. Stein, 2023. "Linear-Cost Covariance Functions for Gaussian Random Fields," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 147-164, January.
    9. Jens-peter Kreiss & Efstathios Paparoditis, 2012. "The Hybrid Wild Bootstrap for Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1073-1084, September.
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