On optimality of the orthogonal block design

Ewa Synówka-Bejenka; Stefan Zontek

Discussiones Mathematicae Probability and Statistics (2012)

  • Volume: 32, Issue: 1-2, page 59-68
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Ewa Synówka-Bejenka, and Stefan Zontek. "On optimality of the orthogonal block design." Discussiones Mathematicae Probability and Statistics 32.1-2 (2012): 59-68. <http://eudml.org/doc/271062>.

@article{EwaSynówka2012,
abstract = {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.},
author = {Ewa Synówka-Bejenka, Stefan Zontek},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Experimental design; orthogonal block design; robust estimator; maximum likelihood estimator; A-optimality; D-optimality; experimental design; -optimality; -optimality},
language = {eng},
number = {1-2},
pages = {59-68},
title = {On optimality of the orthogonal block design},
url = {http://eudml.org/doc/271062},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Ewa Synówka-Bejenka
AU - Stefan Zontek
TI - On optimality of the orthogonal block design
JO - Discussiones Mathematicae Probability and Statistics
PY - 2012
VL - 32
IS - 1-2
SP - 59
EP - 68
AB - 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.
LA - eng
KW - Experimental design; orthogonal block design; robust estimator; maximum likelihood estimator; A-optimality; D-optimality; experimental design; -optimality; -optimality
UR - http://eudml.org/doc/271062
ER -

References

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  1. [1] Robust estimation of parameters in a mixed unbalanced model, The Annals of Statistics 24 (1996) 1493-1510 doi: 10.1214/aos/1032298279 
  2. [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 Zbl0809.62025
  3. [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 Zbl0593.62073
  4. [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 Zbl0464.62067
  5. [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 Zbl0792.62024
  6. [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 Zbl0858.62062
  7. [7] J. Kiefer, Optimum experimental designs, Journal of the Rojal Statistical Society. Series B 21 (2) (1959) 272-319. Zbl0108.15303
  8. [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 Zbl0809.62067

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