| Title:
|
Criteria for optimal design of small-sample experiments with correlated observations (English) |
| Author:
|
Pázman, Andrej |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
453-462 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
optimal design |
| Keyword:
|
correlated observations |
| Keyword:
|
random field |
| Keyword:
|
spatial statistics |
| Keyword:
|
information matrix |
| MSC:
|
62K05 |
| MSC:
|
62M10 |
| MSC:
|
62M40 |
| idZBL:
|
Zbl 1134.62055 |
| idMR:
|
MR2377923 |
| . |
| Date available:
|
2009-09-24T20:25:29Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135787 |
| . |
| Reference:
|
[1] Apt M., Welch W. J.: Fisher information and maximum likelihood estimation of covariance parameters in Gaussian stochastic processes.Canad. J. Statist. 26 (1998), 127–137 MR 1624393 |
| Reference:
|
[2] Brimkulov U. N., Krug G. K., Savanov V. L.: Design of Experiments in Investigating Random Fields and Processes.Nauka, Moscow 1986 |
| Reference:
|
[3] Brown L. D.: Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory.(Vol. 9 of Institute of Mathematical Statistics Lecture Notes – Monograph Series.) Institute of Mathematical Statistics, Hayward 1986 Zbl 0685.62002, MR 0882001 |
| Reference:
|
[4] Cresie N. A. C.: Statistics for Spatial Data.Wiley, New York 1993 MR 1239641 |
| Reference:
|
[5] Gauchi J. P., Pázman A.: Design in nonlinear regression by stochastic minimization of functionals of the mean square error matrix.J. Statist. Plann. Inference 136 (2006), 1135–1152 MR 2181993 |
| Reference:
|
[6] Harman R.: Minimal efficiency of designs under the class of orthogonally invariant information criteria.Metrika 60 (2004), 137–153 Zbl 1079.62072, MR 2088736 |
| Reference:
|
[7] Müller W. G., Pázman A.: An algorithm for computation of optimum designs under a given covariance structure.Comput. Statist. 14 (1999), 197–211 MR 1712010 |
| Reference:
|
[8] Pázman A.: Probability distribution of the multivariate nonlinear least squares estimates.Kybernetika 20 (1984), 209–230 MR 0763647 |
| Reference:
|
[9] Pázman A.: Nonlinear Statistical Models.Kluwer, Dordrecht – Boston 1993 Zbl 0808.62058 |
| Reference:
|
[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 |
| Reference:
|
[11] Pázman A., Pronzato L.: Nonlinear experimental design based on the distribution of estimators.J. Statist. Plann. Inference 33 (1992), 385–402 Zbl 0772.62042, MR 1200655 |
| Reference:
|
[12] Pukelsheim F.: Optimal Design of Experiments.Wiley, New York 1993 Zbl 1101.62063, MR 1211416 |
| Reference:
|
[13] Sacks J., Welch W. J., Mitchell T. J., Wynn H. P.: Design and analysis of computer experiments.Statist. Sci. 4 (1989), 409–435 Zbl 0955.62619, MR 1041765 |
| Reference:
|
[14] Spivak M.: Calculus on Manifolds.W. A. Benjamin, Inc., Menlo Park, Calif. 1965 Zbl 0381.58003, MR 0209411 |
| Reference:
|
[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 Zbl 1082.62514 |
| . |
