On optimality of the orthogonal block design

• Autorzy: Ewa Synówka-Bejenka , Stefan Zontek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Experimental design; orthogonal block design; robust estimator; maximum likelihood estimator; A-optimality; D-optimality

Kategorie tematyczne

• 62K05: Optimal designs
• 62G35: Robustness

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2012
• Tom: 32
• Numer: 1-2
• Strony: 59-68

Daty

wydano

2012

otrzymano

2012-06-01

Twórcy

autor

Ewa Synówka-Bejenka

• Faculty of Mathematics, Computer Science and Ekonometrics, University of Zielona Góra, prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland

autor

Stefan Zontek

• Faculty of Mathematics, Computer Science and Ekonometrics, University of Zielona Góra, prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland

Bibliografia

• [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

Identyfikatory

DOI

10.7151/dmps1144