Bernoulli

  • 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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 18 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1179498756

Digital Object Identifier
doi:10.3150/07-BEJ5093

Mathematical Reviews number (MathSciNet)
MR2331259

Zentralblatt MATH identifier
1127.62087

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

Citation

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. https://projecteuclid.org/euclid.bj/1179498756


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