Estimation in semiparametric spatial regression
AbstractNonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For spatial data on a grid evaluating the conditional mean given its closest neighbors requires a four-dimensional nonparametric regression. In this paper a semiparametric spatial regression approach is proposed to avoid this problem. An estimation procedure based on combining the so-called marginal integration technique with local linear kernel estimation is developed in the semiparametric spatial regression setting. Asymptotic distributions are established under some mild conditions. The same convergence rates as in the one-dimensional regression case are established. An application of the methodology to the classical Mercer and Hall wheat data set is given and indicates that one directional component appears to be nonlinear, which has gone unnoticed in earlier analyses.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 11971.
Date of creation: May 2003
Date of revision:
Publication status: Published in The Annals of Statistics 3.34(2006): pp. 1395-1435
Additive approximation; asymptotic theory; conditional autoregression; local linear kernel estimate; marginal integration; semiparametric regression; spatial mixing process;
Other versions of this item:
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
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- Marc Hallin & Zudi Lu & Lanh T. Tran, 2004.
"Kernel density estimation for spatial processes: the L1 theory,"
ULB Institutional Repository
2013/2127, ULB -- Universite Libre de Bruxelles.
- Hallin, Marc & Lu, Zudi & Tran, Lanh T., 2004. "Kernel density estimation for spatial processes: the L1 theory," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 61-75, January.
- Marc Hallin & Zudi Lu & Lanh T. Tran, 2004. "Local linear spatial regression," ULB Institutional Repository 2013/2131, ULB -- Universite Libre de Bruxelles.
- Sperlich, Stefan & Tj stheim, Dag & Yang, Lijian, 2002.
"Nonparametric Estimation And Testing Of Interaction In Additive Models,"
Cambridge University Press, vol. 18(02), pages 197-251, April.
- Sperlich, Stefan & Tjøstheim, Dag & Yang, Lijian, 1998. "Nonparametric estimation and testing of interaction in additive models," SFB 373 Discussion Papers 1998,14, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Oliver Linton & Enno Mammen & N Nielsen, 2000.
"The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions,"
STICERD - Econometrics Paper Series
/2000/386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
- Lu, Zudi & Chen, Xing, 2004. "Spatial kernel regression estimation: weak consistency," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 125-136, June.
- Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
- Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
- Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
- Marc Hallin & Zudi Lu & Lanh T. Tran, 2001. "Density estimation for spatial linear processes," ULB Institutional Repository 2013/2109, ULB -- Universite Libre de Bruxelles.
- Gao, Jiti & Lu, Zudi & Tjostheim, Dag, 2003. "Semiparametric spatial regression: theory and practice," MPRA Paper 11991, University Library of Munich, Germany, revised Oct 2006.
- Marc Hallin & Michel Carbon & Lanh T. Tran, 1996. "Kernel density estimation on random fields: the L1 theory," ULB Institutional Repository 2013/2065, ULB -- Universite Libre de Bruxelles.
- Patrick Saart & Jiti Gao, 2012. "Semiparametric Methods in Nonlinear Time Series Analysis: A Selective Review," Monash Econometrics and Business Statistics Working Papers 21/12, Monash University, Department of Econometrics and Business Statistics.
- Peter M Robinson, 2011. "Inference on Power Law Spatial Trends (Running Title: Power Law Trends)," STICERD - Econometrics Paper Series /2011/556, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
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