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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