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Gaussian semiparametric estimation Gaussian semiparametric estimation of two-dimensional intrinsically stationary random fields

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  • Yoshihiro Yajima
  • Yasumasa Matsuda

Abstract

We consider Gaussian semiparametric estimation (GSE) for two dimensional intrinsically stationary random fields (ISRFs) observed on a regular grid and derive its asymptotic properties. Originally GSE was proposed to estimate long memory time series models in a semiparametric way either for stationary or nonstationary cases. We try an extension of GSE for time series to anisotropic ISRFs observed on two dimensional lattice that include isotropic fractional Brownian fields (FBF) as special cases, which have been employed to describe many physical spatial behaviours. The GSE extended to ISRFs is consistent and has a limiting normal distribution with variance independent of any unknown parameters as sample size goes to infinity, under conditions we specify in this paper. We conduct a computational simulation to compare the performances of it with those of an alternative estimator on the spatial domain.

Suggested Citation

  • Yoshihiro Yajima & Yasumasa Matsuda, 2023. "Gaussian semiparametric estimation Gaussian semiparametric estimation of two-dimensional intrinsically stationary random fields," DSSR Discussion Papers 136, Graduate School of Economics and Management, Tohoku University.
    • Handle: RePEc:toh:dssraa:136
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    File URL: http://hdl.handle.net/10097/0002000031
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    4. Jacques Istas, 2007. "Identifying the Anisotropical Function of a d-Dimensional Gaussian Self-similar Process with Stationary Increments," Statistical Inference for Stochastic Processes, Springer, vol. 10(1), pages 97-106, January.
    5. Rainer Dahlhaus, 1983. "Spectral Analysis With Tapered Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 163-175, May.
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