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Testing the covariance function of stationary Gaussian random fields

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  • Taheriyoun, Ali Reza

Abstract

In many problems, a specific function like h(⋅) is considered as the covariance function. Based on the asymptotic distribution of the periodogram and Euler characteristic, three methods are introduced to test the equality of the covariance function with h(⋅). Our analyses prove the accuracy of the power and scaling laws for the covariance function of metal surfaces.

Suggested Citation

  • Taheriyoun, Ali Reza, 2012. "Testing the covariance function of stationary Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 606-613.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:606-613
    DOI: 10.1016/j.spl.2011.11.014
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    References listed on IDEAS

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    1. Fuentes, Montserrat, 2005. "A formal test for nonstationarity of spatial stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 30-54, September.
    2. Taheriyoun, Ali Reza & Shafie, Khalil & Jozani, Mohammad Jafari, 2009. "A note on the higher moments of the Euler characteristic of the excursion sets of random fields," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1074-1082, April.
    3. Robert Lund & Hany Bassily & Brani Vidakovic, 2009. "Testing equality of stationary autocovariances," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 332-348, May.
    4. D. S. Coates & P. J. Diggle, 1986. "Tests For Comparing Two Estimated Spectral Densities," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 7-20, January.
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