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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1144,
author = {Ewa Syn\'owka-Bejenka and Stefan Zontek},
title = {On optimality of the orthogonal block design},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {32},
year = {2012},
pages = {59-68},
zbl = {06248587},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1144}
}
Ewa Synówka-Bejenka; Stefan Zontek. On optimality of the orthogonal block design. Discussiones Mathematicae Probability and Statistics, Tome 32 (2012) pp. 59-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1144/
[000] [1] Robust estimation of parameters in a mixed unbalanced model, The Annals of Statistics 24 (1996) 1493-1510 doi: 10.1214/aos/1032298279
[001] [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 | Zbl 0809.62025
[002] [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 | Zbl 0593.62073
[003] [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 | Zbl 0464.62067
[004] [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 | Zbl 0792.62024
[005] [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 | Zbl 0858.62062
[006] [7] J. Kiefer, Optimum experimental designs, Journal of the Rojal Statistical Society. Series B 21 (2) (1959) 272-319. | Zbl 0108.15303
[007] [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 | Zbl 0809.62067