• Bernoulli
  • Volume 13, Number 2 (2007), 447-472.

Exploring spatial nonlinearity using additive approximation

Zudi Lu, Arvid Lundervold, Dag Tjøstheim, and Qiwei Yao

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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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Bernoulli, Volume 13, Number 2 (2007), 447-472.

First available in Project Euclid: 18 May 2007

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additive approximation α-mixing asymptotic normality auto-normal specification backfitting nonparametric kernel estimation spatial models uniform convergence


Lu, Zudi; Lundervold, Arvid; Tjøstheim, Dag; Yao, Qiwei. Exploring spatial nonlinearity using additive approximation. Bernoulli 13 (2007), no. 2, 447--472. doi:10.3150/07-BEJ5093.

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