Open Access
May 2007 Exploring spatial nonlinearity using additive approximation
Zudi Lu, Arvid Lundervold, Dag Tjøstheim, Qiwei Yao
Bernoulli 13(2): 447-472 (May 2007). DOI: 10.3150/07-BEJ5093


We propose to approximate the conditional expectation of a spatial random variable given its nearest-neighbour observations by an additive function. The setting is meaningful in practice and requires no unilateral ordering. It is capable of catching nonlinear features in spatial data and exploring local dependence structures. Our approach is different from both Markov field methods and disjunctive kriging. The asymptotic properties of the additive estimators have been established for $α$-mixing spatial processes by extending the theory of the backfitting procedure to the spatial case. This facilitates the confidence intervals for the component functions, although the asymptotic biases have to be estimated via (wild) bootstrap. Simulation results are reported. Applications to real data illustrate that the improvement in describing the data over the auto-normal scheme is significant when nonlinearity or non-Gaussianity is pronounced.


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Zudi Lu. Arvid Lundervold. Dag Tjøstheim. Qiwei Yao. "Exploring spatial nonlinearity using additive approximation." Bernoulli 13 (2) 447 - 472, May 2007.


Published: May 2007
First available in Project Euclid: 18 May 2007

zbMATH: 1127.62087
MathSciNet: MR2331259
Digital Object Identifier: 10.3150/07-BEJ5093

Keywords: Additive approximation , asymptotic normality , auto-normal specification , backfitting , nonparametric kernel estimation , Spatial models , Uniform convergence , α-mixing

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability

Vol.13 • No. 2 • May 2007
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