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dc.contributor.authorTeunissen, Peter.
dc.date.accessioned2017-01-30T13:24:29Z
dc.date.available2017-01-30T13:24:29Z
dc.date.created2011-10-24T03:51:23Z
dc.date.issued2007
dc.identifier.citationTeunissen, PJG. 2007. Least squares prediction in linear models with integer unknowns. Journal of Geodesy. 81(9): pp. 565-579.
dc.identifier.urihttp://hdl.handle.net/20.500.11937/31274
dc.identifier.doi10.1007/s00190-007-0138-0
dc.description.abstract

The prediction of spatially and/or temporal varying variates based on observations of these variates at some locations in space and/or instances in time, is an important topic in the various spatial and Earth sciences disciplines. This topic has been extensively studied, albeit under different names. The underlying model used is often of the trend-signal-noise type. This model is quite general and it encompasses many of the conceivable measurements. However, the methods of prediction based on these models have only been developed for the case the trend parameters are real-valued. In the present contribution we generalize the theory of least-squares prediction by permitting some or all of the trend parameters to be integer valued. We derive the solution for least-squares prediction in linear models with integer unknowns and show how it compares to the solution of ordinary least-squares prediction. We also study the probabilistic properties of the associated estimation and prediction errors. The probability density functions of these errors are derived and it is shown how they are driven by the probability mass functions of the integer estimators. Finally, we show how these multimodal distributions can be used for constructing confidence regions and for cross-validation purposes aimed at testing the validity of the underlying model.

dc.languageen
dc.subjectInteger Based Least Squares Prediction - Integer Estimation - Least Squares Collocation - Model - Multimodal Distribution - Real Integer Mixed Linear
dc.titleLeast squares prediction in linear models with integer unknowns.
dc.typeJournal Article
curtin.note

The original publication is available at: http://www.springerlink.com

curtin.departmentDepartment of Spatial Sciences
curtin.accessStatusFulltext not available


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