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Criteria for optimal design of small-sample experiments with correlated observations. (English) Zbl 1134.62055
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 the estimators. We mention briefly expressions obtained for very small samples via the probability densities of the estimators. Then we show that an approximation of MSE via the Fisher information matrix is possible, even for small or moderate samples, when the errors of the 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.

62K05 Optimal statistical designs
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M40 Random fields; image analysis
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