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Local Whittle estimator for anisotropic random fields

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  • Guo, Hongwen
  • Lim, Chae Young
  • Meerschaert, Mark M.

Abstract

A local Whittle estimator is developed to simultaneously estimate the long memory parameters for stationary anisotropic scalar random fields. It is shown that these estimators are consistent and asymptotically normal, under some weak technical conditions. A brief simulation study illustrates a practical application of the estimator.

Suggested Citation

  • Guo, Hongwen & Lim, Chae Young & Meerschaert, Mark M., 2009. "Local Whittle estimator for anisotropic random fields," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 993-1028, May.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:993-1028
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    References listed on IDEAS

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    1. Biermé, Hermine & Meerschaert, Mark M. & Scheffler, Hans-Peter, 2007. "Operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 312-332, March.
    2. Leonenko, N.N. & Sakhno, L.M., 2006. "On the Whittle estimators for some classes of continuous-parameter random processes and fields," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 781-795, April.
    3. Dahlhaus, Rainer, 1985. "Asymptotic normality of spectral estimates," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 412-431, June.
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    Cited by:

    1. Abry, Patrice & Didier, Gustavo, 2018. "Wavelet eigenvalue regression for n-variate operator fractional Brownian motion," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 75-104.
    2. Hira Koul & Nao Mimoto & Donatas Surgailis, 2016. "A goodness-of-fit test for marginal distribution of linear random fields with long memory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 165-193, February.
    3. Surgailis, Donatas, 2020. "Scaling transition and edge effects for negatively dependent linear random fields on Z2," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7518-7546.
    4. Puplinskaitė, Donata & Surgailis, Donatas, 2015. "Scaling transition for long-range dependent Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2256-2271.
    5. Lihong Wang & Jinde Wang, 2014. "Wavelet estimation of the memory parameter for long range dependent random fields," Statistical Papers, Springer, vol. 55(4), pages 1145-1158, November.
    6. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2017. "Scaling transition for nonlinear random fields with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2751-2779.
    7. Lim, C.Y. & Meerschaert, M.M. & Scheffler, H.-P., 2014. "Parameter estimation for operator scaling random fields," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 172-183.
    8. Didier, Gustavo & Meerschaert, Mark M. & Pipiras, Vladas, 2018. "Domain and range symmetries of operator fractional Brownian fields," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 39-78.
    9. Patrice Abry & Gustavo Didier & Hui Li, 2019. "Two-step wavelet-based estimation for Gaussian mixed fractional processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 157-185, July.
    10. Robinson, Peter, 2019. "Spatial long memory," LSE Research Online Documents on Economics 102182, London School of Economics and Political Science, LSE Library.
    11. Wang, Lihong, 2009. "Memory parameter estimation for long range dependent random fields," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2297-2306, November.
    12. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.
    13. Nicolis, Orietta & Ramírez-Cobo, Pepa & Vidakovic, Brani, 2011. "2D wavelet-based spectra with applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 738-751, January.
    14. Burnecki, Krzysztof & Sikora, Grzegorz, 2017. "Identification and validation of stable ARFIMA processes with application to UMTS data," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 456-466.
    15. Angela Ferretti & L. Ippoliti & P. Valentini & R. J. Bhansali, 2023. "Long memory conditional random fields on regular lattices," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    16. Beran, Jan & Ghosh, Sucharita & Schell, Dieter, 2009. "On least squares estimation for long-memory lattice processes," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2178-2194, November.

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