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Properties of spatial cross-periodograms using fixed-domain asymptotics

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  • Lim, Chae Young
  • Stein, Michael

Abstract

Cross-periodograms can be used to study a multivariate spatial process observed on a lattice. For spatial data, it is often appropriate to study asymptotic properties of statistical procedures under fixed-domain asymptotics in which the number of observations increases in a fixed region while shrinking distances between neighboring observations. Using fixed-domain asymptotics, we prove relative asymptotic unbiasedness and relative consistency of a smoothed cross-periodogram after appropriate filtering of the data. In addition, we show that smoothed cross-periodograms are asymptotically normal when the process is stationary multivariate Gaussian with appropriate assumptions on high-frequency behavior of the spectral density.

Suggested Citation

  • Lim, Chae Young & Stein, Michael, 2008. "Properties of spatial cross-periodograms using fixed-domain asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1962-1984, October.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:9:p:1962-1984
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    References listed on IDEAS

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    1. István Fazekas & Alexey Chuprunov, 2006. "Asymptotic Normality of Kernel Type Density Estimators for Random Fields," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 161-178, July.
    2. Hao Zhang & Dale L. Zimmerman, 2005. "Towards reconciling two asymptotic frameworks in spatial statistics," Biometrika, Biometrika Trust, vol. 92(4), pages 921-936, December.
    3. Montserrat Fuentes, 2002. "Spectral methods for nonstationary spatial processes," Biometrika, Biometrika Trust, vol. 89(1), pages 197-210, March.
    4. Furrer, Reinhard, 2005. "Covariance estimation under spatial dependence," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 366-381, June.
    5. Jun Zhu & S. Lahiri, 2007. "Bootstrapping the Empirical Distribution Function of a Spatial Process," Statistical Inference for Stochastic Processes, Springer, vol. 10(2), pages 107-145, July.
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    Cited by:

    1. Zhou, Yuzhen & Xiao, Yimin, 2018. "Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 56-72.
    2. 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.
    3. Guinness, Joseph, 2022. "Nonparametric spectral methods for multivariate spatial and spatial–temporal data," Journal of Multivariate Analysis, Elsevier, vol. 187(C).

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