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Some Inference Results for Causal Autoregressive Processes on a Plane

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  • Jiin‐Huarng Guo
  • L. Billard

Abstract

We investigate the causal autoregressive process on a plane pioneered by Whittle (On stationary processes on the plane. Biometrika 41 (1954), 434–49) and further studied by Besag (Spatial interaction and statistical analysis of lattice systems. J. R. Stat. Soc. Ser. B 36 (1974), 192–236). We develop test statistics to test composite hypotheses about the parameters and to test if the process is separable. Also, when some data points are missing, we develop a computational procedure obtained by combining the EM algorithm and bootstrap procedures to find estimates of the parameters and hence the distribution of these estimates.

Suggested Citation

  • Jiin‐Huarng Guo & L. Billard, 1998. "Some Inference Results for Causal Autoregressive Processes on a Plane," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(6), pages 681-691, November.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:6:p:681-691
    DOI: 10.1111/1467-9892.00116
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    Cited by:

    1. Ojeda, Silvia & Vallejos, Ronny & Bustos, Oscar, 2010. "A new image segmentation algorithm with applications to image inpainting," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2082-2093, September.
    2. Abdelouahab Bibi & Karima Kimouche, 2014. "On stationarity and second-order properties of bilinear random fields," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 221-244, October.

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