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Asymptotic theory for nonparametric regression with spatial data

Robinson, Peter (2011) Asymptotic theory for nonparametric regression with spatial data. Journal of Econometrics, 165 (1). pp. 5-19. ISSN 0304-4076

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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 the application of our conditions to spatial autoregressive models, and models defined on a regular lattice.

Item Type: Article
Official URL: http://www.elsevier.com/wps/find/journaldescriptio...
Additional Information: © 2011 Elsevier B.V.
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Journal of Economic Literature Classification System: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C13 - Estimation
C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C14 - Semiparametric and Nonparametric Methods
C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C21 - Cross-Sectional Models; Spatial Models; Treatment Effect Models
Sets: Departments > Economics
Collections > Economists Online
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 20 Oct 2011 15:07
URL: http://eprints.lse.ac.uk/39004/

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