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Fourier analysis of irregularly spaced data on Rd

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  • Yasumasa Matsuda
  • Yoshihiro Yajima

Abstract

Summary. The purpose of the paper is to propose a frequency domain approach for irregularly spaced data on Rd. We extend the original definition of a periodogram for time series to that for irregularly spaced data and define non‐parametric and parametric spectral density estimators in a way that is similar to the classical approach. Introduction of the mixed asymptotics, which are one of the asymptotics for irregularly spaced data, makes it possible to provide asymptotic theories to the spectral estimators. The asymptotic result for the parametric estimator is regarded as a natural extension of the classical result for regularly spaced data to that for irregularly spaced data. Empirical studies are also included to illustrate the frequency domain approach in comparisons with the existing spatial and frequency domain approaches.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:1:p:191-217
    DOI: 10.1111/j.1467-9868.2008.00685.x
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    References listed on IDEAS

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    1. 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.
    2. Engle, Robert F, 1974. "Band Spectrum Regression," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 1-11, February.
    3. Michael L. Stein & Zhiyi Chi & Leah J. Welty, 2004. "Approximating likelihoods for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 275-296, May.
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    Cited by:

    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. Tata Subba Rao & Granville Tunnicliffe Wilson & Soutir Bandyopadhyay & Carsten Jentsch & Suhasini Subba Rao, 2017. "A Spectral Domain Test for Stationarity of Spatio-Temporal Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 326-351, March.
    3. Delgado, Miguel A. & Robinson, Peter M., 2015. "Non-nested testing of spatial correlation," Journal of Econometrics, Elsevier, vol. 187(1), pages 385-401.
    4. Sam Efromovich, 2014. "Efficient Non-Parametric Estimation Of The Spectral Density In The Presence Of Missing Observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 407-427, August.
    5. Giovanna Jona Lasinio & Gianluca Mastrantonio & Alessio Pollice, 2013. "Discussing the “big n problem”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(1), pages 97-112, March.
    6. Kurisu, Daisuke, 2019. "On nonparametric inference for spatial regression models under domain expanding and infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    7. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    8. 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).
    9. Robinson, Peter, 2019. "Spatial long memory," LSE Research Online Documents on Economics 102182, London School of Economics and Political Science, LSE Library.
    10. Salim Bouzebda & Inass Soukarieh, 2022. "Non-Parametric Conditional U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 11(1), pages 1-69, December.
    11. repec:cep:stiecm:/2013/568 is not listed on IDEAS
    12. Salim Bouzebda, 2024. "Limit Theorems in the Nonparametric Conditional Single-Index U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 12(13), pages 1-81, June.
    13. Arthur P. Guillaumin & Adam M. Sykulski & Sofia C. Olhede & Frederik J. Simons, 2022. "The Debiased Spatial Whittle likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1526-1557, September.
    14. Gupta, A, 2015. "Autoregressive Spatial Spectral Estimates," Economics Discussion Papers 14458, University of Essex, Department of Economics.
    15. Zhang, Shibin, 2020. "Nonparametric Bayesian inference for the spectral density based on irregularly spaced data," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    16. Yasumasa Matsuda, 2013. "Generalized Whittle Estimate For Nonstationary Spatial Data," TERG Discussion Papers 305, Graduate School of Economics and Management, Tohoku University.

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