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Parameter estimation for operator scaling random fields

Author

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  • Lim, C.Y.
  • Meerschaert, M.M.
  • Scheffler, H.-P.

Abstract

Operator scaling random fields are useful for modeling physical phenomena with different scaling properties in each coordinate. This paper develops a general parameter estimation method for such fields which allows an arbitrary set of scaling axes. The method is based on a new approach to nonlinear regression with errors whose mean is not zero.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:172-183
    DOI: 10.1016/j.jmva.2013.09.010
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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. Houdré, C. & Kawai, R., 2006. "On fractional tempered stable motion," Stochastic Processes and their Applications, Elsevier, vol. 116(8), pages 1161-1184, August.
    3. Leonenko, N.N. & Petherick, S. & Sikorskii, A., 2012. "A normal inverse Gaussian model for a risky asset with dependence," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 109-115.
    4. 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.
    5. Bhattacharyya, B. B. & Khoshgoftaar, T. M. & Richardson, G. D., 1992. "Inconsistent M-estimators: nonlinear regression with multiplicative error," Statistics & Probability Letters, Elsevier, vol. 14(5), pages 407-411, July.
    6. 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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    Cited by:

    1. Zhang, Yong & Sun, HongGuang & Stowell, Harold H. & Zayernouri, Mohsen & Hansen, Samantha E., 2017. "A review of applications of fractional calculus in Earth system dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 29-46.
    2. Lee, Jeonghwa, 2021. "Hurst estimation for operator scaling random fields," Statistics & Probability Letters, Elsevier, vol. 178(C).

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