A three-dimensional unilateral autoregressive lattice process

Journal of Statistical Planning and Inference

Volumn 59, Issue 1, 1997, Pages 1-18

  Martin, R J ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Autoregressive processes; Lattice processes; Spatial processes; Unilateral processes

Indexed keywords

EID: 0031498433     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(96)00090-0     Document Type: Article

References (18)

1. Abramowitz, M. and I.A. Stegun, Eds. (1965). Handbook of Mathematical Functions. Dover, New York.
2. Basu, S. and G.C. Reinsel (1992). A note on properties of spatial Yule-Walker estimators. J. Statist. Comput. Simul. 41, 243-255.
3. Basu, S. and G.C. Reinsel (1993). Properties of the spatial unilateral first-order ARMA model. Adv. Appl. Probab. 25, 631-648.
4. Besag, J.E. (1972). On the correlation structure of some two-dimensional stationary processes. Biometrika 59, 43-48.
5. Besag, J.E. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussion). J. Roy. Statist. Soc. B 36, 192-236.
6. Besag, J. (1981). On a system of two-dimensional recurrence equations. J. Roy. Statist. Soc. B 43, 302-309.
7. Guyon, X. (1982). Parameter estimation for a stationary process on a d-dimensional lattice. Biometrika 69, 95-105.
8. Ha, E. and H.J. Newton (1993). The bias of estimators of causal spatial autoregressive processes. Biometrika 80, 242-245.
9. Martin, R.J. (1979). A subclass of lattice processes applied to a problem in planar sampling. Biometrika 66, 209-217.
10. Martin, R.J. (1990). The use of time series models and methods in the analysis of agricultural field trials. Commun. Statist. -Theory Meth. 19, 55-81.
11. Martin, R.J. (1996). Some results on unilateral ARMA lattice processes. J. Statist. Plann. Inference 50, 395-411.
12. Pickard, D.K. (1980). Unilateral Markov fields. Adv. Appl. Probab. 12, 655-671.
13. Politis, D.N. (1994). Markov chains in many dimensions. Adv. Appl. Probab. 26, 756-774.
14. Riordan, J. (1968). Combinatorial Identities. Krieger, Huntingdon, New York.
15. Sharp, W.E. and L.A. Aroian (1985). The generation of multidimensional autoregressive series by the herringbone method. Math. Geol. 17, 67-79.
16. Tjøstheim, D. (1978). Statistical spatial series modelling. Adv. Appl. Probab. 10, 130-154. Correction (1984) 16, 220.
17. Tory, E.M. and D.K. Pickard (1992). Unilateral Gaussian fields. Adv. Appl. Probab. 24, 95-112.
18. Whittle, P. (1954). On stationary processes in the plane. Biometrika 41, 434-449.