Estimation in semiparametric spatial regression

By Jiti Gao, Zudi Lu, Dag Tjøstheim. 2006

90 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/3d7033b0ccd7752c67518f0ef5eafc15a45406e8

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In Economics and Econometrics

1. Yiguo Sun
2. Jiti Gao
3. Dag Tjøstheim
4. Zudi Lu
5. Maxwell L. King
6. Marc Hallin
7. Wenyang Zhang
8. Keming Yu

Citations in the corpus

• NONPARAMETRIC SPECIFICATION TESTING FOR NONLINEAR TIME SERIES WITH NONSTATIONARITY (2009, unknown): “Additional details are available from Appendixes B–D of the original version by Gao et al. (2007).”
• A semiparametric spatial dynamic model (2014, background): “[6]; Kelejian and Prucha [8]; Ord [12]; Su and Jin [13]) and varying coefficient models (Cheng et al.”
• Specification testing in nonlinear and nonstationary time series autoregression (2009, methodology): “lar forms have been used for the stationary time series case [see, e.g., Hjellvik, Yao and Tjøstheim (1998)]. Other alternatives to NT(h), including the introduction of MT (h) below, are discussed in Gao et al. (2006). In theory, we can derive a test statistic based on NT(h). As can be seen, NT(h) i”
• Functional-coefficient spatial autoregressive models with nonparametric spatial weights (2016, methodology): “Note that our model is related to but di¤erent from the models studied in the existing literature of semiparametric spatial regression models with additive structure (e.g., Gao et al., 2006, Lu et al., 2007).”
• Local linear spatial quantile regression (2009, background): “Several recent papers (among which [48], [49], [8], [22] and [23], are dealing with the related problem of estimating the density f of a random fleld of the form fXi ; i 2ZNg; whereas [24], [35], [36], and [ 19 ] consider the estimation”