Exploring spatial nonlinearity using additive approximation
Lu, Zudi; Lundervold, Arvid; Tjostheim, Dag; Yao, Qiwei
Source PublicationBERNOULLI
AbstractWe propose to approximate the conditional expectation of a spatial random variable given its nearestneighbour 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 alpha-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.
Keywordadditive approximation alpha-mixing asymptotic normality auto-normal specification backfitting nonparametric kernel estimation spatial models uniform convergence
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000247425700007
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Document Type期刊论文
Corresponding AuthorLu, Zudi
Affiliation1.Univ London London Sch Econ & Polit Sci, Dept Stat, London WC2A 2AE, England
2.Chinese Acad Sci, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
3.Univ Bergen, Dept Physiol, N-5007 Bergen, Norway
4.Univ Bergen, Dept Math, N-5007 Bergen, Norway
5.Peking Univ, Guanghua Sch Management, Beijing 100871, Peoples R China
6.Curtin Univ Technol, Dept Math & Stat, Perth, WA 6001, Australia
Recommended Citation
GB/T 7714
Lu, Zudi,Lundervold, Arvid,Tjostheim, Dag,et al. Exploring spatial nonlinearity using additive approximation[J]. BERNOULLI,2007,13(2):447-472.
APA Lu, Zudi,Lundervold, Arvid,Tjostheim, Dag,&Yao, Qiwei.(2007).Exploring spatial nonlinearity using additive approximation.BERNOULLI,13(2),447-472.
MLA Lu, Zudi,et al."Exploring spatial nonlinearity using additive approximation".BERNOULLI 13.2(2007):447-472.
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