Abstract
A new class of lattice models, whose joint densities are products of unilateral conditional densities, is introduced. Maximum likelihood estimation, for causal conditional exponential families on a two dimensional lattice, is discussed. The technique proposed enables one to construct a rich class of lattice models with a parsimoneous parameterization.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bartlett, M. S. (1978). Nearest neighbour models in the analysis of field experiments. J. Roy. Statist. Soc. B 40, 147–158.
Basawa, I. V., Brockwell, P. J. and Mandrekar, V. (1992). Inference for spatial time series. Interface-90 Proceedings 301–302, Springer-Verlag, New York.
Basawa, I. V., Feigin, P. D. and Heyde, C. C. (1976). Asymptotic properties of maximum likelihood estimators for stochastic processes. Sanlhya A, 38, 259–270.
Basawa, I. V. and Prakasa Rao, B. L. S. (1980). Statistical Inference for Stochastic Processes. Academic Press, London.
Basawa, I. V. and Scott, D. J. (1993). Asymptotic Optimal Inference for Non-eryodic Models. Lecture Notes in Statistics, Vol 17, Springer-Verlag, New York.
Basu, S. and Reinsel, G. C. (1993). Properties of the spatial unilateral first order ARMA model. Adv. Appl. Prob. 25, 631–648.
Besag, J. E. (1974). Spatial interaction and the statistical analysis of lattice systems. J. Roy. Statist. Soc. B 36, 192–225.
Cliff, A. D. and Ord, J. K. (1975). Model building and analysis of spatial pattern in human geography. J. Roy. Statist. Soc. B 37, 297–328.
Cressie, N. A. C. (1991). Statistics for Spatial Data Wiley, New York.
Greyer, C. J. (1992). Practical Markov chain Monte Carlo (with discussion). Statist. Sci. 7, 473–511.
Guyon, Y. (1995). Random Field on a Network: Modeling Statistics and Applications Springer-Verlag, New York.
Haining, R. P. (1979). Statistical tests and process generators for random field models. Geographical Analysis 11 45–64.
Hall, P. and Heyde, C. C. (1980). Martingale Limit Theory and Its Application. Academic Press, New York.
Pickard, D. K. (1980). Unilateral Markov fields. Adv. Appl. Prob. 12, 655–671.
Pickard, D. K. (1987). Inference for discrete Markov fields: The simplest nontrivial case. J. Amer. Statist. Assn. 82, 90–96.
Tjostheim, D. (1978). Statistical spatial series modeling. Adv. Appl. Prob. 10, 130–154.
Tjostheim, D. (1983). Statistical spatial series modelling II: Some further results on unilateral lattice processes. Adv. Appl. Prob. 15, 562–584.
Whittle, P. (1954). On stationary processes in the plane. Biometrika 41, 434–449.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this paper
Cite this paper
Basawa, I.V. (1996). Inference for a Class of Causal Spatial Models. In: Heyde, C.C., Prohorov, Y.V., Pyke, R., Rachev, S.T. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0749-8_28
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0749-8_28
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94788-4
Online ISBN: 978-1-4612-0749-8
eBook Packages: Springer Book Archive