Criteria for optimal design of small-sample experiments with correlated observations

Andrej Pázman

Kybernetika (2007)

  • Volume: 43, Issue: 4, page 453-462
  • ISSN: 0023-5954

Abstract

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We consider observations of a random process (or a random field), which is modeled by a nonlinear regression with a parametrized mean (or trend) and a parametrized covariance function. Optimality criteria for parameter estimation are to be based here on the mean square errors (MSE) of estimators. We mention briefly expressions obtained for very small samples via probability densities of estimators. Then we show that an approximation of MSE via Fisher information matrix is possible, even for small or moderate samples, when the errors of observations are normal and small. Finally, we summarize some properties of optimality criteria known for the noncorrelated case, which can be transferred to the correlated case, in particular a recently published concept of universal optimality.

How to cite

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Pázman, Andrej. "Criteria for optimal design of small-sample experiments with correlated observations." Kybernetika 43.4 (2007): 453-462. <http://eudml.org/doc/33870>.

@article{Pázman2007,
abstract = {We consider observations of a random process (or a random field), which is modeled by a nonlinear regression with a parametrized mean (or trend) and a parametrized covariance function. Optimality criteria for parameter estimation are to be based here on the mean square errors (MSE) of estimators. We mention briefly expressions obtained for very small samples via probability densities of estimators. Then we show that an approximation of MSE via Fisher information matrix is possible, even for small or moderate samples, when the errors of observations are normal and small. Finally, we summarize some properties of optimality criteria known for the noncorrelated case, which can be transferred to the correlated case, in particular a recently published concept of universal optimality.},
author = {Pázman, Andrej},
journal = {Kybernetika},
keywords = {optimal design; correlated observations; random field; spatial statistics; information matrix; spatial statistics; information matrix},
language = {eng},
number = {4},
pages = {453-462},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Criteria for optimal design of small-sample experiments with correlated observations},
url = {http://eudml.org/doc/33870},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Pázman, Andrej
TI - Criteria for optimal design of small-sample experiments with correlated observations
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 4
SP - 453
EP - 462
AB - We consider observations of a random process (or a random field), which is modeled by a nonlinear regression with a parametrized mean (or trend) and a parametrized covariance function. Optimality criteria for parameter estimation are to be based here on the mean square errors (MSE) of estimators. We mention briefly expressions obtained for very small samples via probability densities of estimators. Then we show that an approximation of MSE via Fisher information matrix is possible, even for small or moderate samples, when the errors of observations are normal and small. Finally, we summarize some properties of optimality criteria known for the noncorrelated case, which can be transferred to the correlated case, in particular a recently published concept of universal optimality.
LA - eng
KW - optimal design; correlated observations; random field; spatial statistics; information matrix; spatial statistics; information matrix
UR - http://eudml.org/doc/33870
ER -

References

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  10. Pázman A., Correlated Optimum Design with Parametrized Covariance Function: Justification of the Use of the Fisher Information Matrix and of the Method of Virtual Noise, Research Report No. 5, Institut für Statistik, WU Wien, Vienna 2004 
  11. Pázman A., Pronzato L., Nonlinear experimental design based on the distribution of estimators, J. Statist. Plann. Inference 33 (1992), 385–402 (1992) Zbl0772.62042MR1200655
  12. Pukelsheim F., Optimal Design of Experiments, Wiley, New York 1993 Zbl1101.62063MR1211416
  13. Sacks J., Welch W. J., Mitchell T. J., Wynn H. P., Design and analysis of computer experiments, Statist. Sci. 4 (1989), 409–435 (1989) Zbl0955.62619MR1041765
  14. Spivak M., Calculus on Manifolds, W. A. Benjamin, Inc., Menlo Park, Calif. 1965 Zbl0381.58003MR0209411
  15. Uciński D., Atkinson A. C., Experimental design for time-dependent models with correlated observations, Stud. Nonlinear Dynamics & Econometrics 8 (2004), Issue 2, Article 13 Zbl1082.62514

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