Previous |  Up |  Next


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:
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


Files Size Format View
Kybernetika_43-2007-4_6.pdf 690.3Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo