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Exploring spatial nonlinearity using additive approximation

Lu, Zudi, Lundervold, Arvid, Tjøstheim, Dag and Yao, Qiwei (2007) Exploring spatial nonlinearity using additive approximation. Bernoulli, 13 (2). pp. 447-472. ISSN 1350-7265

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Identification Number: 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.

Item Type: Article
Official URL:
Additional Information: © 2007 Bernoulli Society for Mathematical Statistics and Probability
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 13 Jun 2008 09:16
Last Modified: 20 Jul 2021 02:02
Projects: 70271003, 70221001
Funders: Leverhulme Trust, National Natural Science Foundation of China

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