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June 2006 Estimation in semiparametric spatial regression
Jiti Gao, Zudi Lu, Dag Tjøstheim
Ann. Statist. 34(3): 1395-1435 (June 2006). DOI: 10.1214/009053606000000317


Nonparametric 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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Jiti Gao. Zudi Lu. Dag Tjøstheim. "Estimation in semiparametric spatial regression." Ann. Statist. 34 (3) 1395 - 1435, June 2006.


Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1113.62048
MathSciNet: MR2278362
Digital Object Identifier: 10.1214/009053606000000317

Primary: 62G05
Secondary: 60J25 , 62J02

Keywords: Additive approximation , Asymptotic theory , conditional autoregression , local linear kernel estimate , marginal integration , semiparametric regression , spatial mixing process

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 3 • June 2006
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