Information contained in design points of experiments with correlated observations

Andrej Pázman

Kybernetika (2010)

  • Volume: 46, Issue: 4, page 771-783
  • ISSN: 0023-5954

Abstract

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A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points. The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this information is zero. Explicit expressions are obtained for the amount of information coming from a selected subset of a given design. Relations to some algorithms for optimum design of experiments in case of correlated observations are indicated.

How to cite

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Pázman, Andrej. "Information contained in design points of experiments with correlated observations." Kybernetika 46.4 (2010): 771-783. <http://eudml.org/doc/196442>.

@article{Pázman2010,
abstract = {A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points. The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this information is zero. Explicit expressions are obtained for the amount of information coming from a selected subset of a given design. Relations to some algorithms for optimum design of experiments in case of correlated observations are indicated.},
author = {Pázman, Andrej},
journal = {Kybernetika},
keywords = {optimal sampling design; spatial statistics; random process; nonlinear regression; information matrix; optimal sampling design; spatial statistics; random process; nonlinear regression; information matrix},
language = {eng},
number = {4},
pages = {771-783},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Information contained in design points of experiments with correlated observations},
url = {http://eudml.org/doc/196442},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Pázman, Andrej
TI - Information contained in design points of experiments with correlated observations
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 4
SP - 771
EP - 783
AB - A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points. The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this information is zero. Explicit expressions are obtained for the amount of information coming from a selected subset of a given design. Relations to some algorithms for optimum design of experiments in case of correlated observations are indicated.
LA - eng
KW - optimal sampling design; spatial statistics; random process; nonlinear regression; information matrix; optimal sampling design; spatial statistics; random process; nonlinear regression; information matrix
UR - http://eudml.org/doc/196442
ER -

References

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  4. Fedorov, V. V., Müller, W. G., Optimum design for correlated fields via covariance kernel expansions, In: Model Oriented Data and Analysis 8, (J. Lopez-Fidalgo, J. H. Rodriguez-Diaz, and B. Torsney, eds.), Physica-Verlag, Heidelberg 2007, pp. 57–66. (2007) MR2409030
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  9. Näther, W., 10.1080/02331888508801879, Statistics 16 (1985), 479–484. (1985) MR0803486DOI10.1080/02331888508801879
  10. Pázman, A., Criteria for optimal design of small-sample experiments with correlated observations, Kybernetika 43 (2007), 453–462. (2007) Zbl1134.62055MR2377923
  11. Pukelsheim, F., Optimal Design of Experiments, Wiley, New York 1993. (1993) Zbl0834.62068MR1211416
  12. Sacks, J., Ylvisaker, D., 10.1214/aoms/1177699599, Ann. Math. Statist. 37 (1966), 66–84. (1966) MR0192601DOI10.1214/aoms/1177699599
  13. Zimmerman, D. L., 10.1002/env.769, Environmetrics 17 (2006), 635–652. (2006) MR2247174DOI10.1002/env.769

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