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Generalized Whittle Estimate For Nonstationary Spatial Data

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  • Yasumasa Matsuda

Abstract

This paper considers analysis of nonstationary irregularly spaced data that may have multivariate observations. The nonstationarity we focus on here means a local dependency of parameters that describe covariance structures. Nonparametric and parametric ways to estimate the local dependency of the parameters are proposed by an extension of traditional periodogram for stationary time series to that for nonstationary spatial data We introduce locally stationary processes for which consistency of the estimators are proved as well as demonstrate empirical efficiency of the methods by simulated and real examples.

Suggested Citation

  • Yasumasa Matsuda, 2013. "Generalized Whittle Estimate For Nonstationary Spatial Data," TERG Discussion Papers 305, Graduate School of Economics and Management, Tohoku University.
  • Handle: RePEc:toh:tergaa:305
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    File URL: http://hdl.handle.net/10097/56546
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    References listed on IDEAS

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    1. Kaufman, Cari G. & Schervish, Mark J. & Nychka, Douglas W., 2008. "Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1545-1555.
    2. Sudipto Banerjee & Alan E. Gelfand & Andrew O. Finley & Huiyan Sang, 2008. "Gaussian predictive process models for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 825-848.
    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.
    4. IM, Hae Kyung & Stein, Michael L. & Zhu, Zhengyuan, 2007. "Semiparametric Estimation of Spectral Density With Irregular Observations," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 726-735, June.
    5. Yun Bai & Peter X.-K. Song & T. E. Raghunathan, 2012. "Joint composite estimating functions in spatiotemporal models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(5), pages 799-824, November.
    6. Yasumasa Matsuda & Yoshihiro Yajima, 2009. "Fourier analysis of irregularly spaced data on "R"-super-"d"," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 191-217.
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