Asymptotic theory for nonparametric regression with spatial data
AbstractNonparametric regression with spatial, or spatio-temporal, data is considered. The conditional mean of a dependent variable, given explanatory ones, is a nonparametric function, while the conditional covariance reflects spatial correlation. Conditional heteroscedasticity is also allowed, as well as non-identically distributed observations. Instead of mixing conditions, a (possibly non-stationary) linear process is assumed for disturbances, allowing for long range, as well as short-range, dependence, while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities. A basic triangular array setting is employed, with the aim of covering various patterns of spatial observation. Sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates. When the cross-sectional dependence is sufficiently mild, the asymptotic variance in the central limit theorem is the same as when observations are independent; otherwise, the rate of convergence is slower. We discuss the application of our conditions to spatial autoregressive models, and models defined on a regular lattice.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 165 (2011)
Issue (Month): 1 ()
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Web page: http://www.elsevier.com/locate/jeconom
Nonparametric regression; Spatial data; Weak dependence; Long range dependence; Heterogeneity; Consistency; Central limit theorem;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
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- Jenish, Nazgul, 2012. "Nonparametric spatial regression under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 167(1), pages 224-239.
- Jungyoon Lee & Peter M Robinson, 2013. "Series Estimation under Cross-sectional Dependence," STICERD - Econometrics Paper Series /2013/570, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Robinson, Peter M. & Thawornkaiwong, Supachoke, 2012. "Statistical inference on regression with spatial dependence," Journal of Econometrics, Elsevier, vol. 167(2), pages 521-542.
- Miguel A. Delgado & Peter M Robinson, 2013. "Non-Nested Testing of Spatial Correlation," STICERD - Econometrics Paper Series /2013/568, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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