Additional Selected Topics

  • Erkki P. Liski
  • Nripes K. Mandal
  • Kirti R. Shah
  • Bikas K. Sinha
Part of the Lecture Notes in Statistics book series (LNS, volume 163)


Models: Competing effects model, split block model, nested model, 3-way classification model, Poisson count model Optimality criteria: Universal optimality (UO), A- D- and E-optimality Major tools: Complete symmetry and trace maximization [Kiefer’s Proposition 1] Optimality results: Characterization of UO designs in different settings Thrust: Diverse applications of UO and balancing

In this Chapter, we dwell on some design settings and present the underlying optimal designs, covering UO or specific optimality criteria viz., A-, D- and E-optimality. The purpose is to acquaint the readers with a variety of interesting and non-standard application areas of optimal designs. We specially mention (i) competing effects model, (ii) split block designs and (iii) models with heteroscedastic errors. In addition, (iv) nested designs and (v) 3-way balanced designs are also discussed.


Information Matrix Balance Incomplete Block Design Column Effect Heteroscedastic Error Nest Factor 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abdelbasit, K. M. and Plackett, R. L. (1983). Experimental design for binary data. Journal of the American Statistical Association 78, 90–98.MathSciNetzbMATHCrossRefGoogle Scholar
  2. Agrawal, H. L. (1966). Some systematic methods of construction of designs for two-way elimination of heterogeneity. Calcutta Statistical Association Bulletin 15, 93–108.MathSciNetzbMATHGoogle Scholar
  3. Atkinson, A. C. and Cook, R. D. (1995). D-optimum designs for heteroscedastic linear models. Journal of the American Statistical Association 90, 204–212.MathSciNetzbMATHGoogle Scholar
  4. Bagchi, S. and Shah, K. R. (1989). On the optimality of a class of rowcolumn designs. Journal of Statistical Planning and Inference 23, 397–402.MathSciNetzbMATHCrossRefGoogle Scholar
  5. Bagchi, S., Mukhopadhyay, A. C. and Sinha, Bikas K. (1990). A search for optimal nested row-column designs. Sankhya, Series B 52, 93–104.MathSciNetzbMATHGoogle Scholar
  6. Bhaumik, D. K. (1995). Optimality in the competing effects model. Sankhya 57, 48–56.MathSciNetzbMATHGoogle Scholar
  7. Das, K., Mandai, N. K. and Sinha, Bikas K. (2000). de la Garza phenomenon re-visited: Part II: Optimal designs under heteroscedastic errors in linear regression. Submitted to Statistics and Probability Letters.Google Scholar
  8. Ford, I., Torsney, B. and Wu, C. F. J. (1992). The use of a canonical form in the construction of locally optimal designs for non-linear problems. Journal of the Royal Statistical Society, Series 54, 569–583.MathSciNetzbMATHGoogle Scholar
  9. Heiligers, B. and Sinha, Bikas K. (1995). Optimality aspects of Agrawal designs — Part II. Statistica Sinica 5, 599–604.MathSciNetzbMATHGoogle Scholar
  10. Hedayat, A. S. and Raghavarao, D. (1975). 3-way BIB designs. Journal of Combinatorial Theory, Series A 18, 207–209.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Hedayat, A. S., Yan, B. and Pezzuto, J. M. (1997). Modeling and identifying optimum designs for fitting dose-response curves based on raw optical density data. Journal of the American Statistical Association 92, 1132–1140.MathSciNetzbMATHCrossRefGoogle Scholar
  12. Khan, M. K. and Yazdi, A. A. (1988). On D-optimal designs for binary data. Journal of Statistical Planning and Inference 18, 83–91.MathSciNetzbMATHCrossRefGoogle Scholar
  13. Kiefer, J. C. (1975). Construction and optimality of generalized Youden designs. In A Survey of Statistical Design and Linear Models. Ed. J. N. Srivastava. North — Holland, Amsterdam. 333–353.Google Scholar
  14. Mandai, N. K., Shah, K. R. and Sinha, Bikas K. (2000). de la Garze phenomenon re-visited. Submitted to Metrika.Google Scholar
  15. Mathew, T. and Sinha, Bikas K. (2001). Optimal designs for binary data under logistic regression. Journal of Statistical Planning and Inference 93, 295–307MathSciNetzbMATHCrossRefGoogle Scholar
  16. Minkin, S. (1987). Optimal design for binary data. Journal of the American Statistical Association 82, 1098–1103.MathSciNetCrossRefGoogle Scholar
  17. Minkin, S. (1993). Experimental design for clonogenic assessment in chemotherapy. Journal of American Statistical Association 88, 410–420.MathSciNetCrossRefGoogle Scholar
  18. Morgan, J. P. (1996). Nested Designs. In Handbook of Statistics, 13 (Design and Analysis of Experiments). Ed. S. Ghosh and C. R. Rao. North Holland, Amsterdam. 939–976.Google Scholar
  19. Ozawa, K., Jimbo, M., Kageyama, S. and Mejza, S. (2001). Optimality and construction of incomplete split-block designs. To appear in Journal of Statistical Planning and Inference.Google Scholar
  20. Pukelsheim, F. (1993). Optimal design of experiments. Wiley, New York.zbMATHGoogle Scholar
  21. Raghavarao, D., Federer, W. T. and Schwager, S. J. (1986). Characteristics for distinguishing balanced incomplete block designs with repeated blocks. Journal of Statistical Planning and Inference 13, 151–163.MathSciNetzbMATHCrossRefGoogle Scholar
  22. Raghavarao, D. and Zhou, B. (1998). Universal optimality of UE 3-designs for a competing effects model. Communications in Statistics — Theory and Methods 27(1), 153–164.MathSciNetzbMATHCrossRefGoogle Scholar
  23. Saharay, R. (1996). A class of optimal row-column designs with some empty cells. Statistica Sinica 6, 989–996.MathSciNetzbMATHGoogle Scholar
  24. Sebastiani, P. and Settimmi, R. (1997). A note on D-optimal designs for a logistic regression model. Journal of Statistical Planning and Inference 59, 359–368.MathSciNetzbMATHCrossRefGoogle Scholar
  25. Shah, K. R. (2000). Optimal split-block designs. Unpublished Manuscript.Google Scholar
  26. Shah, K. R. and Sinha, Bikas K. (1990). Optimality aspects of Agrawal designs. Gujarat Statistical Review: Professor C. G. Khatri Memorial Volume 7, 214–222.Google Scholar
  27. Shah, K. R. and Sinha, Bikas K. (1996). Row-column designs. In Handbook of Statistics 13: Design and Analysis of Experiments. Ed. S. Ghosh and C. R. Rao. North Holland, 903–938.Google Scholar
  28. Shah, K. R. and Sinha, Bikas K. (2001a). Discrete optimal designs: Criteria and characterizations. To appear in Recent Advances in Experimental Designs and Related Topics (Proceedings of a Symposium held in Honour of Professor D. Raghavarao in Temple University in October, 1999). Nova Science Publishers, 115–133.Google Scholar
  29. Shah, K. R. and Sinha, Bikas K. (2001b). Nested experimental designs. Encyclopedia of Environmetrics. Wiley, New York.Google Scholar
  30. Singh, M. and Dey, A. (1979). Block designs with nested rows and columns. Biometrika 66, 321–327.MathSciNetzbMATHCrossRefGoogle Scholar
  31. Sitter, R. R. and Wu, C. F. J. (1993). Optimal designs for binary response experiments: Fieller-, D, and A criteria. Scandinavian Journal of Statistics 20, 329–342.MathSciNetzbMATHGoogle Scholar
  32. Srivastava, J. N. (1978). Statistical design of agricultural experiments. Journal of Indian Society of Agricultural Statististics 30, 1–10.Google Scholar
  33. Wu, C. F. J. (1988). Optimal design for percentile estimation of a quantal response curve. In Optimal Design and Analysis of Experiments, Eds. Y. Dodge, V. Federov and H. P. Wynn. Elsevier, Amsterdam, 213–223.Google Scholar
  34. Yeh, C. M. (1986). Condition for universal optimality of block designs. Biometrika 73, 701–706.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Erkki P. Liski
    • 2
  • Nripes K. Mandal
    • 1
  • Kirti R. Shah
    • 4
  • Bikas K. Sinha
    • 3
  1. 1.Department of StatisticsCalcutta UniversityCalcuttaIndia
  2. 2.Department of Mathematics, Statistics, and PhilosophyUniversity of TampereTampereFinland
  3. 3.Stat-Math DivisonIndian Statistical InstituteCalcuttaIndia
  4. 4.Department of Statistics and Actuarial ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations