Estimation in semiparametric spatial regression

Annals of Statistics

Volumn 34, Issue 3, 2006, Pages 1395-1435

  Gao, Jiti ^a   Lu, Zudi ^b,d,e   Tjøstheim, Dag ^c  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^c UNIVERSITY OF BERGEN   (Norway)

^d INSTITUTE OF SYSTEMS SCIENCE   (China)

^e LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Additive approximation; Asymptotic theory; Conditional autoregression; Local linear kernel estimate; Marginal integration; Semiparametric regression; Spatial mixing process

Indexed keywords

EID: 33747152153     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053606000000317     Document Type: Article

References (37)

1. BESAG, J. E. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussion). J. Roy. Statist. Soc. Ser. B 36 192-236. MR0373208
2. BJERVE, S. and DOKSUM, K. (1993). Correlation curves: Measures of association as functions of covariate values. Ann. Statist. 21 890-902. MR1232524
3. BOLTHAUSEN, E. (1982). On the central limit theorem for stationary mixing random fields. Ann. Probab. 10 1047-1050. MR0672305
4. 1 theory. J. Nonparametr. Statist. 6 157-170. MR1383049
5. CHILES, J.-P. and DELFINER, P. (1999). Geostatistics: Modeling Spatial Uncertainty. Wiley, New York. MR1679557
6. CRESSIE, N. A. C. (1993). Statistics for Spatial Data. Wiley, New York. MR1239641
7. FAN, J. and GIJBELS, I. (1996). Local Polynomial Modelling and Its Applications. Chapman and Hall, London. MR1383587
8. FAN, J., HÄRDLE, W. and MAMMEN, E. (1998). Direct estimation of low-dimensional components in additive models. Ann. Statist. 26 943-971. MR1635422
9. GAO, J. (1998). Semiparametric regression smoothing of nonlinear time series. Scand. J. Statist. 25 521-539. MR1649952
10. GAO, J. and KING, M. L. (2005). Estimation and model specification testing in nonparametric and semiparametric regression models. Unpublished report. Available at www.maths.uwa.edu.au/~jiti/jems.pdf.
11. GAO, J., LU, Z. and TJØSTHEIM, D. (2005). Semiparametric spatial regression: Theory and practice. Unpublished technical report. Available at www.maths.uwa.edu.au/-jiti/glt05.pdf.
12. GUYON, X. (1995). Random Fields on a Network. Modeling, Statistics and Applications. Springer, New York. MR1344683
13. GUYON, X. and RICHARDSON, S. (1984). Vitesse de convergence du théorème de la limite centrale pour des champs faiblement dépendants. Z. Wahrsch. Verw. Gebiete 66 297-314. MR0749228
14. HALLIN, M., LU, Z. and TRAN, L. T. (2001). Density estimation for spatial linear processes. Bernoulli 7 657-668. MR1849373
15. 1 theory. J. Multivariate Anal. 88 61-75. MR2021860
16. HALLIN, M., Lu, Z. and TRAN, L. T. (2004). Local linear spatial regression. Ann. Statist. 32 2469-2500. MR2153992
17. HÄRDLE, W., LIANO, H. and GAO, J. (2000). Partially Linear Models. Physica-Verlag, Heidelberg. MR1787637
18. HENOARTNER, N. W. and SPERLICH, S. (2003). Rate optimal estimation with the integration method in the presence of many covariates. Available at www.rnaths.uwa.edu.au/-jiti/hs.pdf.
19. JONES, M. C. and KOCH, I. (2003). Dependence maps: Local dependence in practice. Statist. Comput. 13 241-255. MR1982478
20. LIN, Z. and Lu, C. (1996). Limit Theory for Mixing Dependent Random Variables. Kluwer, Dordrecht. MR1486580
21. Lu, Z. and CHEN, X. (2002). Spatial nonparametric regression estimation: Non-isotropic case. Acta Math. Appl. Sinica English Ser. 18 641-656. MR2012328
22. LU, Z. and CHEN, X. (2004). Spatial kernel regression estimation: Weak consistency. Statist. Probab. Lett. 68 125-136. MR2066167
23. LU, Z., LUNDERVOLD, A., TJØSTHEIM, D. and YAO, Q. (2005). Exploring spatial nonlinearity using additive approximation. Discussion paper, Dept. Statistics, London School of Economics, London. Available at www.maths.uwa.edu.au/~jiti/11ty.pdf.
24. MAMMEN, E., LINTON, O. and NIELSEN, J. P. (1999). The existence and asymptotic properties of a backfilling projection algorithm under weak conditions. Ann. Statist. 27 1443-1490. MR1742496
25. MCBRATNEY, A. B. and WEBSTER, R. (1981). Detection of ridge and furrow pattern by spectral analysis of crop yield. Internat. Statist. Rev. 49 45-52.
26. MERCER, W. B. and HALL, A. D. (1911). The experimental error of field trials. J. Agricultural Science 4 107-132.
27. NIELSEN, J. P. and LINTON, O. B. (1998). An optimization interpretation of integration and back-fitting estimators for separable nonparametric models. J. R. Stat. Soc. Ser. B Stat. Methodol. 60 217-222. MR1625624
28. POSSOLO, A., ed. (1991). Spatial Statistics and Imaging. IMS, Hayward, CA. MR1195556
29. RVOIRARD, J. (1994). Introduction to Disjunctive Kriging and Non-Linear Geostatistics. Clarendon Press, Oxford.
30. ROSENBLATT, M. (1985). Stationary Sequences and Random Fields. Birkhäuser, Boston. MR0885090
31. SPERLICH, S., TJØSTHEIM, D. and YANG, L. (2002). Nonparametric estimation and testing of interaction in additive models. Econometric Theory 18 197-251. MR1891823
32. STEIN, M. L. (1999). Interpolation of Spatial Data. Some Theory for Kriging. Springer, New York. MR1697409
33. TRAN, L. T. (1990). Kernel density estimation on random fields. J. Multivariate Anal. 34 37-53. MR1062546
34. TRAN, L. T. and YAKOWITZ, S. (1993). Nearest neighbor estimators for random fields. J. Multivariate Anal. 44 23-46. MR1208468
35. WACKERNAGEL, H. (1998). Multivariate Geostatistics: An Introduction With Applications, 2nd ed. Springer, Berlin.
36. WHITTLE, P. (1954). On stationary processes in the plane. Biometrika 41 434-449. MR0067450
37. WHITTLE, P. (1963). Stochastic process in several dimensions. Bull. Inst. Internat. Statist. 40 974-994. MR0173287