Geodesic
On optimality of the orthogonal block design
Discussiones Mathematicae. Probability and Statistics, Tome 32 (2012) no. 1-2, pp. 59-68.

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In the paper a usual block design with treatment effects fixed and block effects random is considered. To compare experimental design the asymptotic covariance matrix of a robust estimator proposed by Bednarski and Zontek (1996) for simultaneous estimation of shift and scale parameters is used. Asymptotically A- and D- optimal block designs in the class of designs with bounded block sizes are characterized.
Keywords: Experimental design, orthogonal block design, robust estimator, maximum likelihood estimator, A-optimality, D-optimality 
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Synówka-Bejenka, Ewa; Zontek, Stefan. On optimality of the orthogonal block design. Discussiones Mathematicae. Probability and Statistics, Tome 32 (2012) no. 1-2, pp. 59-68. http://geodesic.mathdoc.fr/item/DMPS_2012_32_1-2_a4/

[1] Robust estimation of parameters in a mixed unbalanced model, The Annals of Statistics 24 (1996) 1493-1510 doi: 10.1214/aos/1032298279

[2] T. Bednarski and S. Zontek, A note on robust estimation of parameters in mixed unbalanced models, in: Proceedings of the International Conference on Linear Statistical Inference LINSTAT'93, Caliński and Kala (Ed(s)), (Dortrecht: Kluwer Academic Publishers 1994) 87-95

[3] K. Christof and F. Pukelsheim, Approximate design theory for a simple block design with random block effects, Linear Statistical Inference. Lecture Notes in Statistics Vol. 35, Caliński and Klonecki (Ed(s)), (Berlin: Springer-Verlag 1985) 20-28

[4] N. Gaffke and O. Krafft, D-optimum designs for the interblock model, in: Mathematical Statistics and Probability Theory, Lecture Notes in Statistics Vol. 2, Klonecki, Kozek and Rosiński (Ed(s)), (New York: Springer-Verlag 1980) 134-143

[5] Optimum robust estimation of linear aspects in conditionally contaminated linear models, The Annals of Statistics 20 (1992) 331-350 doi: 10.1214/aos/1176348525

[6] S. Kageyama and R. Zmyslony, Characterization and optimality of block designs with estimation of parameters under mixed models, Statistical Sciences and Data Analysis (1993) 559-570

[7] J. Kiefer, Optimum experimental designs, Journal of the Rojal Statistical Society. Series B 21 (2) (1959) 272-319.

[8] R. Zmyślony and S. Zontek, Optimality of the orthogonal block design for robust estimation under mixed models, in: Proceedings of the International Conference on Linear Statistical Inference LINSTAT'93, Caliński and Kala (Ed(s)), (Dortrecht: Kluwer Academic Publishers 1994) 195-202