# W-Iterations and Ripples Therefrom

Chapter

## Summary

The focus of this contribution is on algorithms for constructing optimal designs. Henry Wynn, one of the earliest contributors in this field, inspired David Silvey to point me in the direction of further algorithmic developments. I first heard of this topic at a seminar David gave at University College London in the autumn of 1970 in which he spoke of Henry's work (he had been Henry's external examiner). Henry also attended this seminar! The rest is history. In this chapter, Henry's work and ripples therefrom will be explored.

## Keywords

Maximum Likelihood Estimator Support Point Multiplicative Algorithm Conditional Design Maximum Likelihood Estimation Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## References

- Atwood, C.L. (1976). Convergent design sequences for sufficiently regular optimality criteria. The Annals of Statistics, 4, 1124–1138.MATHCrossRefMathSciNetGoogle Scholar
- Fedorov, V.V. (1972). Theory of Optimal Experiments. Academic Press, New York.Google Scholar
- Fellman, J. (1974). On the allocation of linear observations. Commentationes Physico-Mathematicae, 44, 27–78.Helsinki,MathSciNetGoogle Scholar
- Harman, R. and Pronzato, L. (2007). Improvements on removing non-optimal support points in
*D.*-optimum design algorithms Statistics & Probability Letters, 77, 90–94.MATHCrossRefMathSciNetGoogle Scholar - Kiefer, J. (1974). General equivalence theory for optimum designs (approximate theory). The Annals of Statistics, bf 2, 849–879.CrossRefMathSciNetGoogle Scholar
- Mandal, S. and Torsney, B. (2000). Algorithms for the construction of optimizing distributions. Communications in Statistics – Theory and Methods, 29, 1219–1231.MATHCrossRefMathSciNetGoogle Scholar
- Mandal, S. and Torsney, B. (2006). Construction of optimal designs using a clustering approach. Journal of Statistical Planning and Inference, 136, 1120–1134.MATHCrossRefMathSciNetGoogle Scholar
- Mandal, S., Torsney, B., and Carriere, K.C. (2005). Constructing optimal designs with constraints. Journal of Statistical Planning and Inference, 128, 609–621.MATHCrossRefMathSciNetGoogle Scholar
- Martin-Martin, R., Torsney, B., and Lopez-Fidalgo, J. (2007). Construction of marginally and conditionally restricted designs using multiplicative algorithms. Computational Statistics and Data Analysis, 51, 5547–5561.MATHCrossRefMathSciNetGoogle Scholar
- Pronzato, L. (2003). Removing non-optimal support points in
*D.*-optimum design algorithms Statistics & Probability Letters, 63, 223–228.MATHCrossRefMathSciNetGoogle Scholar - Silvey, S.D., Titterington, D.M., and Torsney, B. (1978). An algorithm for optimal designs on a finite design space. Communications in Statistics A, 7, 1379–1389.CrossRefGoogle Scholar
- Titterington, D.M. (1975). Optimal design: some geometrical aspects of
*D.*-optimality Biometrika, 62, 313–320.MATHMathSciNetGoogle Scholar - Titterington, D.M. (1976). Algorithms for computing
*D.*-optimal designs on a finite design spaceConference on Information Sciences and Systems, Department of Electrical Engineering, Johns Hopkins University, Baltimore, MD, 213–216.Google Scholar - Torsney, B. (1977). Contribution to discussion of a paper by Dempster, Laird and Rubin. Journal of the Royal Statistical Society B, 39, 22–27.Google Scholar
- Torsney, B. (1983). A moment inequality and monotonicity of an algorithm, (Kortanek, K.O. and Fiacco, A.V., eds.). Proceedings of the International Symposium on Semi-Infinite Program and Application 215, University of Texas, Austin. 249–260.Lecture Notes in Economics and Mathematical System,Google Scholar
- Torsney, B. (1988). Computing optimising distributions with applications in design, estimation, and image processing. (Dodge, Y., Fedorov, V.V. and Wynn, H.P., eds.). Optimal Design and Analysis of Experiments Elsevier Science Publishers B. V., North Holland, 361–370.Google Scholar
- Torsney, B. and Alahmadi, A. (1992). Further development of algorithms for constructing optimizing distributions. (Fedorov, V.V., Muller, W.G., and Vuchkov, I.N., eds.). Model Oriented Data Analysis. Physica-Verlag, Wurzburg (Wien), 121–129.Proceedings of the second IIASA Workshop in St. Kyrik, BulgariaGoogle Scholar
- Torsney, B. and Alahmadi, A. (1995). Designing for minimally dependent observations. Statistica Sinica, 5, 499–514.MATHMathSciNetGoogle Scholar
- Torsney, B. and Mandal, S. (2001). Construction of constrained optimal designs, (Atkinson, A., Bogacka, B., and Zhigljavsky, A.A., eds.). Optimum Design 2000, Kluwer, Dordecht, 141–152.Google Scholar
- Torsney, B. and Mandal, S. (2004). Multiplicative algorithms for constructing optimizing distributions: further developments.
*mODa 7 – Advances in Model Oriented Design and Analysis*, Proceedings of seventh International Workshop on Model Oriented Design and Analysis, Heeze, Netherlands, June 14–18, 2004, (Bucchiano, A.D., Lauter, H. and Wynn, H.P., eds.). Physica-Verlag, Heidelberg, 143–150Google Scholar - Torsney, B. and Mandal, S. (2007). Two classes of multiplicative algorithms for constructing optimizing distributions.
*Computational Statistics and Data Analysis*,**51**(3), 1592–1601.MathSciNetGoogle Scholar - Whittle, P. (1973). Some general points in the theory of optimal experimental design. Journal of the Royal Statistical Society B, 35, 123–1390.MATHMathSciNetGoogle Scholar
- Wu, C.F.J. (1978). Some iterative procedures for generating non-singular optimal designs. Communications in Statistics A, 7, 1399–1412.CrossRefGoogle Scholar
- Wu, C.F.J. and Wynn, H.P. (1978). The convergence of general step-length algorithms for regular optimum design criteria. The Annals of Mathematical Statistics, 6, 1273–1285.MATHMathSciNetGoogle Scholar
- Wynn, H.P. (1972). Results in the theory and construction of D-optimum experimental designs (with discussion). Journal of the Royal Statistical Society B, 34, 170–186, 133–147.Google Scholar

## Copyright information

© Springer Science+Business Media LLC 2009