Exploring spatial nonlinearity using additive approximation
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 l...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
International Statistical Institute/Bernoulli Society
2007
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| Online Access: | http://isi.cbs.nl/bernoulli/index.htm http://hdl.handle.net/20.500.11937/20467 |
| _version_ | 1848750312802746368 |
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| author | Lu, Zudi Lundervold, A. Tjostheim, D. YAO, Qiwei |
| author_facet | Lu, Zudi Lundervold, A. Tjostheim, D. YAO, Qiwei |
| author_sort | Lu, Zudi |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T07:34:50Z |
| format | Journal Article |
| id | curtin-20.500.11937-20467 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:34:50Z |
| publishDate | 2007 |
| publisher | International Statistical Institute/Bernoulli Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-204672017-01-30T12:19:27Z Exploring spatial nonlinearity using additive approximation Lu, Zudi Lundervold, A. Tjostheim, D. YAO, Qiwei 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. 2007 Journal Article http://hdl.handle.net/20.500.11937/20467 http://isi.cbs.nl/bernoulli/index.htm International Statistical Institute/Bernoulli Society restricted |
| spellingShingle | Lu, Zudi Lundervold, A. Tjostheim, D. YAO, Qiwei Exploring spatial nonlinearity using additive approximation |
| title | Exploring spatial nonlinearity using additive approximation |
| title_full | Exploring spatial nonlinearity using additive approximation |
| title_fullStr | Exploring spatial nonlinearity using additive approximation |
| title_full_unstemmed | Exploring spatial nonlinearity using additive approximation |
| title_short | Exploring spatial nonlinearity using additive approximation |
| title_sort | exploring spatial nonlinearity using additive approximation |
| url | http://isi.cbs.nl/bernoulli/index.htm http://hdl.handle.net/20.500.11937/20467 |