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Reducing non-stationary random fields to stationarity and isotropy using a space deformation

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  • Perrin, Olivier
  • Senoussi, Rachid

Abstract

Recently, a model for non-stationary random field , n[greater-or-equal, slanted]2} has been developed. This consists of reducing Z to stationarity and isotropy via a bijective bi-differentiable deformation [Phi] of the index space. We give the form of this deformation under smoothness assumptions on the correlation of Z.

Suggested Citation

  • Perrin, Olivier & Senoussi, Rachid, 2000. "Reducing non-stationary random fields to stationarity and isotropy using a space deformation," Statistics & Probability Letters, Elsevier, vol. 48(1), pages 23-32, May.
    • Handle: RePEc:eee:stapro:v:48:y:2000:i:1:p:23-32
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    References listed on IDEAS

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    1. Perrin, Olivier & Senoussi, Rachid, 1999. "Reducing non-stationary stochastic processes to stationarity by a time deformation," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 393-397, July.
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    Cited by:

    1. Michel Harel & Jean-François Lenain & Joseph Ngatchou-Wandji, 2016. "Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 296-321, June.
    2. Kleiber, William, 2016. "High resolution simulation of nonstationary Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 277-288.
    3. Rachid Senoussi & Emilio Porcu, 2022. "Nonstationary space–time covariance functions induced by dynamical systems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 211-235, March.
    4. Lim, Chae Young & Wu, Wei-Ying, 2022. "Conditions on which cokriging does not do better than kriging," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    5. Jordan Richards & Jennifer L. Wadsworth, 2021. "Spatial deformation for nonstationary extremal dependence," Environmetrics, John Wiley & Sons, Ltd., vol. 32(5), August.

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