Abstract
In this paper the authors put forward a new mixtures regression models with Logarithmic terms[14] to generalize Draper's models[1, 2 or 6] by using Kiefer-Wolfowitz's equivalence theorem[3], Fedorov's and Wynn's method[5]. And we also suggest a method for computer-aided design of combinatorial search[13].
In this study, we have proved and constructed the approximateD-optimal (measure) andD n -optimal (exact) designs by the use of the first and second order mixtures regression models with logarithmic terms in three and four components.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Draper, N. R. and St. John, R. C., Designs in Three and Four Components for Mixtures Models with Inverse Terms,Technometrics,19 (1977), 117–130.
Draper, N. R. and St. John, R. C., A Mixtures Model with Inverse Terms,Technometrics,19 (1977), 37–46.
Keifer, J. and Wolfowitz, J., Optimum Designs in Regression Problems,Ann. Math. Statist.,30 (1959), 271–294;32 (1961), 298–325.
Fedorov, V. V., Theory of Optimal Experiments. Translated and Edited by W. J. Studden, E. M. Klimko, Academic Press, New York, 1972.
Wynn, H. P., Results in the Theory and Construction ofD-optimum Experimental Designs (with discussion),J. Roy. Statist. Soc.,B34 (1972), 133–147 and 170–186.
Cornell, J. A., Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data, Wiley, New York, 1981.
Draper, N. R. and St. John, R. C., Models and Designs for Experiments with Mixtures, I. Background material. Mathematics Research Center Technical Summary Report #1435, University of Wisconsin (also issued as Statistics Department Technical Report No. 360), 1974.
Scheffè, H., The Simplex-centroid Design for Experiments with Mixtures,J. Roy. Statist. Soc.,B25 (1963), 235–263.
Scheffè, H., Experiments with Mixtures,J. Roy. Statist. Soc.,B20 (1958), 344–360.
St. John, R. C. and Draper, N. R.,D-Optimality for Regression Designs: A Review,Technometrics,17 (1975), 15–23.
Mao, S. S., etc., Analysis of Regression and Experimental Designs. Publisher of East China Normal University, Shanghai, 1981.
Zhu, W. Y. etc., Theory of Optimum Design and Its Applications. Liaoning People's Publisher, Shenyang, 1981.
Vuchkov, N., Yontchev, Ch. A. and Damgallev, D. L., ContinuousD-optimal Designs for Experiments with Mixture and Process Variable,Math. Operationsforsch. Statist., Ser. Statistics,14 (1983), 33–51.
Aitchison, J. and Bacon-Shone, J., Log Contrast Models for Experiments with Mixtures.Biometrika,71 (1984), 323–330.
Author information
Authors and Affiliations
Additional information
Projects Supported by the Science Fund of the Chinese Academy of Sciences.
Rights and permissions
About this article
Cite this article
Zhu, W., Hu, C. & Chen, H. D-optimality andD n -optimal designs for mixtures regression models with logarithmic terms. Acta Mathematicae Applicatae Sinica 3, 26–36 (1987). https://doi.org/10.1007/BF02112642
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02112642