Some applications of weighing designs

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SUMMARY

The purpose of this paper is to apply results on weighing designs to the setting of 2m factorial designs. Using weighing designs, we give some proposals for experimental plans. Relevant counterexamples are indicated. Also the results of a simulation study on the existence of weighing designs are presented.

References
  • Banerjee K.S. (1975): Weighing Designs for Chemistry, Medicine. Economics, Operations Research, Statistics. Marcel Dekker Inc., New York.

  • Banerjee T., Mukerjee R. (2008): Optimal factorial designs for cDNA microarray experiments. Ann. Appl. Statist. 2: 366-385.

  • Beckman R.J. (1973). An application of multivariate weighing designs. Communication in Statistics 1(6): 561-565.

  • Box G.E., Hunter J.S., Hunter W.G. (2005). Statistics for Experimenters: Design, Innovation, and Discovery, 2nd Edition. Wiley.

  • Ceranka B., Graczyk M. (2001): Optimum chemical balance weighing designs under the restriction on weighings. Discussiones Mathematicae-Probability and Statistics 21: 111-120.

  • Ceranka B., Graczyk M. (2003): Optimum chemical balance weighing designs for v+1 objects. Kybernetika 39: 333-340.

  • Ceranka B., Katulska K. (1987a): The application of the theory of spring balance weighing design for experiments with mixtures (in Polish). Listy Biometryczne XXIV(1): 17-26.

  • Ceranka B., Katulska K. (1987b): The application of the optimum spring balance weighing designs (in Polish). Siedemnaste Colloquium Metodologiczne z Agro- Biometrii: 98-108.

  • Ceranka B., Katulska K. (1989): Application of the biased spring balance weighing theory to estimation of differences of line effects for legume content. Biometrical Journal 31: 103-110.

  • Ceranka B., Katulska K. (2001): A-optimal chemical balance weighing design with diagonal covariance matrix of errors. Moda 6, Advances in Model Oriented Design and Analysis, A.C. Atkinson, P. Hackl, W.G. Műller, eds., Physica-Verlag, Heidelberg, New York: 29-36.

  • Cheng C.S. (1980): Optimality of some weighing and n 2 fractional factorial designs. Annals of Statistics 8: 436-446.

  • Gawande B.N., Patkar A.Y. (1999): Application of factorial design for optimization of Cyclodextrin Glycosyltransferase production from Klebsiella pneumoniae pneumonaiae AS-22, Biotechnology and Bioengineering 64(2): 168-173.

  • Glonek G.F.V., Solomon P.J. (2004): Factorial and time course designs for cDNA microarray experiments. Biostatistics 5: 89-111.

  • Graczyk M. (2009): Regular A-optimal design matrices X=(xij) xij=-1, 0, 1. Statistical Papers 50: 789-795.

  • Graczyk M. (2011): A-optimal biased spring balance design. Kybernetika 47: 893-901.

  • Graczyk M. (2012a): Notes about A-optimal spring balance weighing design. Journal of Statistical Planning and Inference 142: 781-784.

  • Graczyk M. (2012b): A-optimal spring balance weighing design under some conditions. Communication in Statistics-Theory and Methods 41: 2386-2393

  • Graczyk M. (2012c): Regular A-optimal spring balance weighing designs. Revstat 10(3): 1-11.

  • John P.W.M. (1971): Statistical Design and Analysis of Experiments. Macmillan, New York.

  • Katulska K. (1984): The application of the theory of weighing design for feeding mixtures investigations and in the geodesy (in Polish). Czternaste Colloquium Metodologiczne z Agro-Biometrii: 195-208.

  • Katulska K. (1989): Optimum biased spring balance weighing design. Statistics and Probability Letters 8: 267-271.

  • Kiefer J. (1974): General equivalence theory for optimum designs. The Annals of Statistics 2: 849-879.

  • Koukouvinos Ch. (1995): Optimal weighing designs and some new weighing matrices. Statistics and Probability Letters 25: 37-42.

  • Koukouvinos Ch., Seberry J. (1997): Weighing matrices and their applications. Journal of Statistical Planning and Inference 62: 91-101.

  • Montgomery D.C. (1991): Design and Analysis of Experiments. 3rd edition. John Wiley & Sons, New York.

  • Mukerjee R., Tang B. (2012): Optimal fractions of two-level factorials under a baseline parameterization. Biometrika 99(1): 71-84.

  • Pukelsheim F. (1993): Optimal Design of Experiment. John Wiley & Sons, New York.

  • 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.

  • Seta G., Mrówczyński M., Wachowiak H. (2000): Harmfulness and possibility of pollen beetle control with combined application of insecticides and foliar fertilisers (in Polish). Progress in Plant Protection/Postępy w Ochronie Roślin 40(2): 905-907.

  • Sloane N.J.A., Harwit M. (1976). Masks for Hadamard transform optics, and weighing designs. Applied Optics 15(1): 107-114.

  • Yang Y.H., Speed T. (2002): Design issues for cDNA microarray experiments. Nature Genetics (Suppl.) 3: 579-588.

Biometrical Letters

The Journal of Polish Biometric Society

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