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An L2 -test for comparing spatial spectral densities

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  • Crujeiras, Rosa M.
  • Fernández-Casal, Rubén
  • González-Manteiga, Wenceslao

Abstract

We consider Z1 and Z2 second-order stationary spatial processes. Our goal is to test whether the dependence structure is the same for both processes, that is, H0:f1=f2, where each fl denotes the spectral density of each observed process, for l=1,2. We study the asymptotic distribution for a Cramer-von-Mises type test statistic, under H0 and under local alternatives. A simulation study showing the performance of the test is also provided.

Suggested Citation

  • Crujeiras, Rosa M. & Fernández-Casal, Rubén & González-Manteiga, Wenceslao, 2008. "An L2 -test for comparing spatial spectral densities," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2543-2551, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2543-2551
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    1. King, Eileen & Hart, Jeffrey D. & Wehrly, Thomas E., 1991. "Testing the equality of two regression curves using linear smoothers," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 239-247, September.
    2. Zhang, Chunming & Dette, Holger, 2004. "A power comparison between nonparametric regression tests," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 289-301, February.
    3. Charles Kooperberg & Charles J. Stone & Young K. Truong, 1995. "Rate Of Convergence For Logspline Spectral Density Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(4), pages 389-401, July.
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    Cited by:

    1. Bowman, Adrian W. & Crujeiras, Rosa M., 2013. "Inference for variograms," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 19-31.
    2. Hidalgo, Javier & Seo, Myung Hwan, 2015. "Specification Tests For Lattice Processes," Econometric Theory, Cambridge University Press, vol. 31(2), pages 294-336, April.
    3. Alain, Boudou & Sylvie, Viguier-Pla, 2014. "Structure of the random measure associated with an isotropic stationary process," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 111-128.

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