Parameter estimates for fractional autoregressive spatial processes

Annals of Statistics

Volumn 33, Issue 6, 2005, Pages 2553-2567

  Boissy, Y ^a   Bhattacharyya, B B ^b   Li, X ^a   Richardson, G D ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Autoregressive spatial process; Long memory; Parameter estimation; Spectral density function

Indexed keywords

EID: 33644929675     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053605000000589     Document Type: Article

References (26)

1. BASU, S. (1990). Analysis of first-order spatial bilateral ARMA models. Ph.D. dissertation, Univ. Wisconsin-Madison.
2. BASU, S. and REINSEL, G. C. (1994). Regression models with spatially correlated errors. J. Amer. Statist. Assoc. 89 88-99.
3. BESAG, J. (1981). On a system of two-dimensional recurrence equations. J. Roy. Statist. Soc. Ser. B. 43 302-309. MR0637942
4. BHATTACHARYYA, B. B., KHALIL, T. M. and RICHARDSON, G. D. (1996). Gauss-Newton estimation of parameters for a spatial autoregression model. Statist. Probab. Lett 28 173-179. MR1394671
5. BHATTACHARYYA, B. B., RICHARDSON, G. D. and FRANKLIN, L. A. (1997). Asymptotic inference for near unit roots in spatial autoregression. Ann. Statist. 25 1709-1724. MR1463571
6. BOISSY, Y. (2001). Parametric estimates for fractional autoregressive processes. Ph.D. dissertation, Univ. Central Florida.
7. BROCKWELL, P. J. and DAVIS, R. A. (1991). Time Series: Theory and Methods, 2nd ed. Springer, New York. MR1093459.
8. CULLES, B. R. and GLEESON, A. C. (1991). Spatial analysis of field experiments - an extension to two dimensions. Biometrics 47 1449-1460.
9. DELFINER, P. and DELHOMME, J. P. (1975). Optimum interpolation by kriging. In NATO Advanced Study Institute on Display and Analysis of Spatial Data (J. C. Davis and M. J. McCullagh, eds.) 96-115. Wiley, New York.
10. FAIRFIELD SMITH, H. (1938). An empirical law describing heterogeneity in yields of agricultural crops. J. Agricultural Science 28 1-23.
11. Fox, R. and TAQQU. M. S. (1986). Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14 517-532. MR0840512
12. Fox, R. and TAQQU, M. S. (1987). Central limit theorems for quadratic forms in random variables having long-range dependence. Probab. Theory Related Fields 74 213-240. MR0871252
13. HANNAN, E. J. (1973). The asymptotic theory of linear time-series models. J. Appl. Probability 10 130-145. MR0365960
14. JAIN, A. K. (1981). Advances in mathematical models for image processing. Proc. IEEE 69 502-528.
15. KHALIL, T. M. (1991). A study of the doubly geometric process, stationary cases and a non-stationary case. Ph.D. dissertation, North Carolina State Univ.
16. KIM, K.-Y. and KIM, Y. Y. (2002). Mechanism of Kelvin and Rossby waves during ENSO events. Meteorology and Atmospheric Physics 81 169-189.
17. LIM, Y.-K., KIM, K.-Y, and LEE, H.-S. (2002). Temporal and spatial evolution of the Asian summer monsoon in the seasonal cycle of synoptic fields. J. Climate 15 3630-3644.
18. MARTIN, R. J. (1979). A subclass of lattice processes applied to a problem in planar sampling. Biometrika 66 209-217. MR0548186
19. MARTIN, R. J. (1986). On the design of experiments under spatial correlation. Biometrika 73 247-277. MR0855887
20. PEARCE, S. C. (1976). An examination of Fairfield Smith's law of environmental variation. J. Agricultural Science 87 21-24.
21. TJØSTHEIM, D. (1978). Statistical spatial series modeling. Adv. in Appl. Probability 10 130-154. MR0471224
22. TJØSTHEIM, D. (1981). Autoregressive modeling and spectral analysis of array data in the plane. IEEE Trans. Geoscience and Remote Sensing 19 15-24.
23. WHITTLE, P. (1951). Hypothesis Testing in Time Series Analysis. Almqvist and Wiksell, Uppsala. MR0040634
24. WHITTLE, P. (1956). On the variation of yield variance with plot size. Biometrika 43 337-343. MR0085658
25. WHITTLE, P. (1962). Topographic correlation, power-law covariance functions, and diffusion. Biometrika 49 305-314. MR0181076
26. ZYGMUND, A. (1968). Trigonometric Series 1, 2, 2nd ed. Cambridge Univ. Press. MR0236587