Some D-optimal chemical balance weighing designs: theory and examples
By: Bronisław Ceranka and Małgorzata Graczyk
References
- Banerjee K.S. (1975): Weighing Designs For Chemistry, Medicine, Economics, Operations Research, Statistics. Marcel Dekker Inc., New York.
- Bulutoglu D.A., Ryan K.J. (2009): D-optimal and near D-optimal 2k fractional factorial designs of resolution V, Journal of Statistical Planning and Inference, 139: 16-22.
- Ceranka B., Graczyk M. (2014a): The problem of D-optimality in some experimental designs. International Journal of Mathematics and Computer Application Research 4: 11-18.
- Ceranka B., Graczyk M. (2014b): Construction of the regular D-optimal weighing designs with non-negative correlated errors. Colloquium Biometricum 44: 43-56.
- Ceranka B., Graczyk M. (2015): Relations between ternary designs and D-optimal weighing designs with non-negative correlated errors. Colloquium Biometricum 145: 23-34.
- Cheng C.S. (2014): Optimal biased weighing designs and two-level main-effect plans. Journal of Statistical Theory and Practice 8: 83-99.
- Cheng C.S., Kao M.H. (2015): Optimal experimental designs for fMRI via circulant biased weighing designs. The Annals of Statistics 43: 2565-2587.
- Graczyk M. (2013): Some applications of weighing designs. Biometrical Letters 50(1): 15-26.
- Harville D.A. (1997): Matrix Algebra from a Statistician’s Perspective. Springer-Verlag, New York Inc.
- Harwit M., Sloane N.J.A. (1979): Hadamard transform optics. New York, Academic Press.
- Jacroux M., Wong C.S., Masaro J.C. (1983). On the optimality of chemical balance weighing designs. Journal of Statistical Planning and Inference 8: 231-240.
- Katulska K., Smaga Ł. (2013). A note on D-optimal chemical balance weighing designs and their applications. Colloquium Biometricum 43: 37-45.
- Masaro J., Wong C.S. (2008): D-optimal designs for correlated random vectors. Journal of Statistical Planning and Inference 138: 4093-4106.
- Neubauer G.N., Pace R.G. (2010): D-optimal (0,1)-weighing designs for eight objects. Linear Algebra and its Applications 432: 2634-2657.
- Payne S.E. (1974): On maximizing det(ATA). Discrete Mathematics 10: 145-458.
- Sathe Y.S., Shenoy R.G. (1990): Construction method for some A- and D-optimal weighing designs when N ≡ 3(mod4). Journal of Statistical Planning and Inference 24: 369-375.10.1016/0378-3758(90)90056-Z
- Smaga Ł. (2014): Necessary and sufficient conditions in the problem of D-optimal weighing designs with autocorrelated errors. Statistics and Probability Letters 92:12-16.10.1016/j.spl.2014.04.027
Language: English
Page range: 137 - 154
Published on: Dec 13, 2017
Published by: Polish Biometric Society
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
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© 2017 Bronisław Ceranka, Małgorzata Graczyk, published by Polish Biometric Society
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.