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Title:Asymptotic theory for nonparametric regression with spatial data PDF Logo
Authors:Robinson, Peter M.
Issue Date:2011
Series/Report no.:cemmap working paper CWP11/11
Abstract:Nonparametric 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 application of our conditions to spatial autoregressive models, and models defined on a regular lattice.
Subjects:Nonparametric regression
Spatial data
Weak dependence
Long range dependence
Heterogeneity
Consistency
Central limit theorem
JEL:C13
C14
C21
Persistent Identifier of the first edition:doi:10.1920/wp.cem.2011.1111
Document Type:Working Paper
Appears in Collections:cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)

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