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Articles

On linear prediction for stationary random fields with nonsymmetrical half-plane past

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Pages 5298-5309 | Received 21 Jan 2020, Accepted 10 Oct 2020, Published online: 22 Oct 2020

References

  • Anderson, T. W. 1971. The statistical analysis of time series. New York: Hohn Wiley & Sons.
  • Baran, S., G. Pap, and M. C. van Zuijlen. 2004. Asymptotic inference for an unstable spatial AR model. Statistics 38 (6):465–82.
  • Basu, S., and G. C. Reinsel. 1993. Properties of the spatial unilateral first-order ARMA model. Advances in Applied Probability 25 (3):631–48.
  • Bondon, P. 2001. Recursive relations for multistep prediction of a stationary time series. Journal of Time Series Analysis 22 (4):399–410.
  • Cheng, R. 2015. Prediction of stationary Gaussian random fields with incomplete quarterplane past. Journal of Multivariate Analysis 139:245–58.
  • Cheng, R., and M. Pourahmadi. 1997. Prediction with incomplete past and interpolation of missing values. Statistics & Probability Letters 33 (1997):341–46.
  • Cressie, N. A. 1993. Statistics for spatial data. New York, NY: Wiley.
  • Francos, J. M. 1990. Parametric model for textures in 2-D images. Doctoral diss., D. Sc. diss., Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
  • Francos, J. M., A. Z. Meiri, and B. Porat. 1993. A unified texture model based on a 2-D Wold-like decomposition. IEEE Transactions on Signal Processing 41 (8):2665–78.
  • Hamaz, A. 2019. Prediction of random fields with incomplete quarter-plane past. Communications in Statistics-Theory and Methods 48 (11):2707–16.
  • Hamaz, A., O. Arezki, and F. Achemine. 2020. Impact of missing data on the prediction of random fields. Journal of Applied Statistics 47 (1):132–49.
  • Helson, H., and D. Lowdenslager. 1958. Prediction theory and Fourier series in several variables. Acta Mathematica 99 (0):165–202.
  • Helson, H., and D. Lowdenslager. 1961. Prediction theory and Fourier series in several variables. II. Acta Mathematica 106 (3-4):175–213.
  • Gikhman, I. I., and A. V. Skorokhod. 2004. The theory of stochastic processes II. Germany: Springer Science & Business Media.
  • Goryainov, V. B. 2011. Least-modules estimates for spatial autoregression coefficients. Journal of Computer and Systems Sciences International 50 (4):565–72.
  • Kallianpur, G., and V. Mandrekar. 1982. Nondeterministic random fields and Wold and Halmos decompositions for commuting isometries. Amsterdam: University of North Carolina.
  • Kizilkaya, A. 2007. On the parameter estimation of 2-D moving average random fields. IEEE Transactions on Circuits and Systems II: Express Briefs 54 (11):989–93.
  • Kizilkaya, A. 2008. Computation of the exact Cramer-Rao lower bound for the parameters of a nonsymmetric half-plane 2-D ARMA model. Digital Signal Processing 18 (5):835–43.
  • Kohli, P., and M. Pourahmadi. 2014. Some prediction problems for stationary random fields with quarter-plane past. Journal of Multivariate Analysis 127:112–25.
  • Pourahmadi, M. 1992. Alternating projections and interpolation of stationary processes. Journal of Applied Probability 29 (04):921–31.
  • Tjøstheim, D. 1983. Statistical spatial series modelling II: Some further results on unilateral lattice processes. Advances in Applied Probability 15 (3):562–84.
  • TsePei, C. 1957. On the linear extrapolation of a continuous homogeneous random field. Theory of Probability & Its Applications 2 (1):58–89.
  • Whittle, P. 1954. On stationary processes in the plane. Biometrika 41 (3-4):434–49.

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