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    Exploring spatial nonlinearity using additive approximation

    Access Status
    Fulltext not available
    Authors
    Lu, Zudi
    Lundervold, A.
    Tjostheim, D.
    YAO, Qiwei
    Date
    2007
    Type
    Journal Article
    
    Metadata
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    Citation
    Lu, Zudi and Lundervold, Arvid and Tjostheim, Dag and Yao, Qiwei . 2007. Exploring spatial nonlinearity using additive approximation. Bernoulli 13: pp. 447-472.
    Source Title
    Bernoulli
    Additional URLs
    http://isi.cbs.nl/bernoulli/index.htm
    ISSN
    13507265
    Faculty
    School of Science and Computing
    Department of Mathematics and Statistics
    Faculty of Science and Engineering
    URI
    http://hdl.handle.net/20.500.11937/20467
    Collection
    • Curtin Research Publications
    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.

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