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On the choice of optimality criteria in comparing statistical designs. (English) Zbl 0691.62067
Summary: We formulate in a reasonable sense a class of optimality functionals for comparing feasible statistical designs available in a given setup. It is desired that the optimality functionals reflect symmetric measures of the lack of information contained in the designs being compared. In view of this, J. Kiefer’s [Surv. Stat. Des. Lin. Models, Int. Symp. Fort Collins 1973, 333-353 (1975; Zbl 0313.62057)] universal optimality criterion is seen to rest on stringent conditions, some of which can be relaxed while preserving optimality (in an extended sense) of the so- called balanced designs.

MSC:
62K05 Optimal statistical designs
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[1] Bondar, Universal optimally of experimental designs: Definitions and a criterion, Canad. J. Statist. 11 pp 325– (1983)
[2] Hedayat, Statistics and Related Topics (1981)
[3] Jacroux, Some minimum variance block designs for estimating treatment differences, J. Roy. Statist. Soc. Ser. B 45 pp 70– (1983) · Zbl 0515.62073
[4] Kato, Perturbation Theory for Linear Operators (1966) · Zbl 0148.12601
[5] Kiefer, A Survey of Statistical Design and Linear Models pp 333– (1975)
[6] Magda, C. G. (1979). On E-optimal block designs and Schur optimality. Ph. D. Thesis, University of Illinois at Chicago.
[7] Sinha, On the optimality of some designs, Calcutta Statist. Assoc. Bull. 19 pp 1– (1970) · Zbl 0227.62045
[8] Takeuchi, On the optimality of certain type of PBIB designs, Rep. Statist. Appl. Res. Un. Japan Sci. Engrs. 8 pp 140– (1961) · Zbl 0104.12503
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