Estimation in semiparametric spatial regression. (English) Zbl 1113.62048
Summary: 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 W. B. Mercer and A. D. Hall [J. Agricult. Sci. 4, 107–132 (1911)] wheat data set is given and indicates that one directional component appears to be nonlinear, which has gone unnoticed in earlier analyses.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62M30 | Inference from spatial processes |
| 60J25 | Continuous-time Markov processes on general state spaces |
Keywords:
additive approximation; asymptotic theory; conditional autoregression; local linear kernel estimate; marginal integration; semiparametric regression; spatial mixing processReferences:
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