Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction

Tomáš Mrkvička; François Goreaud; Joël Chadoeuf

Kybernetika (2011)

  • Volume: 47, Issue: 5, page 696-714
  • ISSN: 0023-5954

Abstract

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We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory variables of the local model are estimated through kernel estimation and (iii) a kernel estimator of the result of the parametric model, supposed here to be a Uniformly Minimum Variance Unbiased Estimator derived under the local parametric model when complete and sufficient statistics are available. The comparison is done asymptotically and by simulations in special cases. The procedure for better estimator selection is then illustrated on a real-life data set.

How to cite

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Mrkvička, Tomáš, Goreaud, François, and Chadoeuf, Joël. "Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction." Kybernetika 47.5 (2011): 696-714. <http://eudml.org/doc/196529>.

@article{Mrkvička2011,
abstract = {We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory variables of the local model are estimated through kernel estimation and (iii) a kernel estimator of the result of the parametric model, supposed here to be a Uniformly Minimum Variance Unbiased Estimator derived under the local parametric model when complete and sufficient statistics are available. The comparison is done asymptotically and by simulations in special cases. The procedure for better estimator selection is then illustrated on a real-life data set.},
author = {Mrkvička, Tomáš, Goreaud, François, Chadoeuf, Joël},
journal = {Kybernetika},
keywords = {kernel estimation; marked Poisson process; mean mark estimation; location-dependent mark distribution; segment process; kernel estimation; marked Poisson process; mean mark estimation; location-dependent mark distribution; segment process},
language = {eng},
number = {5},
pages = {696-714},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction},
url = {http://eudml.org/doc/196529},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Mrkvička, Tomáš
AU - Goreaud, François
AU - Chadoeuf, Joël
TI - Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 5
SP - 696
EP - 714
AB - We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory variables of the local model are estimated through kernel estimation and (iii) a kernel estimator of the result of the parametric model, supposed here to be a Uniformly Minimum Variance Unbiased Estimator derived under the local parametric model when complete and sufficient statistics are available. The comparison is done asymptotically and by simulations in special cases. The procedure for better estimator selection is then illustrated on a real-life data set.
LA - eng
KW - kernel estimation; marked Poisson process; mean mark estimation; location-dependent mark distribution; segment process; kernel estimation; marked Poisson process; mean mark estimation; location-dependent mark distribution; segment process
UR - http://eudml.org/doc/196529
ER -

References

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