Optimal Regression Designs in Asymmetric Domains

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


Model(s): Fixed coefficients regression (FCR), random coefficients regression (RCR) models (single factor linear, quadratic and cubic) Experimental domains: [0, 1], [0, h] and (h, H] Optimality criteria: Minimization of optimality functionals Major tools: de la Garza (DLG) phenomenon and Loewner order domination (LOD) of information matrices for search reduction Optimality results: Specific optimal designs under regression models for estimation, prediction and inverse prediction — all under continuous design theory Thrust: Asymmetric experimental domains


Optimal Design Quadratic Regression Experimental Domain Integrate Mean Square Error Information Matrice 
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. Atkinson, A. C. and Donev, A. N. (1992). Optimum experimental design. Oxford, Oxford University Press.Google Scholar
  2. de la Garza, A. (1954). Spacing of information in polynomial estimation. Annals of Mathematical Statistics 25, 123–130.MathSciNetzbMATHCrossRefGoogle Scholar
  3. Kiefer, J. C. (1959). Optimum experimental designs (with discussion). Journal of the Royal Statistical Socciety Series B 21, 272–319.MathSciNetGoogle Scholar
  4. Luoma, A., Mandai, N. K. and Sinha, Bikas K. (2001a). A-optimal cubic and quartic regression designs in asymmetric factor spaces. Submitted to Statistics and Applications. New Delhi.Google Scholar
  5. Luoma, A., Nummi, T. and Sinha, Bikas K. (2001b): Optimal designs in random coefficient cubic regression models. Technical Report A 337, University of Tampere, Finland.Google Scholar
  6. Liski, E. P., Luoma, A., Mandai, N. K. and Sinha, Bikas K. (1997). Optimal design for an inverse prediction problem under random coefficient regression models. Journal of the Indian Society of Agricultural Statistics Vol. XLIX Golden Jubilee Number 1996-1997, 277–288.Google Scholar
  7. Liski, E. P., Luoma, A., Mandai, N. K. and Sinha, Bikas K. (1998). Optimal designs for prediction in random coefficient linear regression models. Journal of Combinatorics, Information and System Sciences (J. N. Srivastava Felicitation Volume), 23(1-4), 1–16.MathSciNetzbMATHGoogle Scholar
  8. Liski, E. P., Luoma, A. and Sinha, Bikas K. (1996). Optimal designs in a random coefficient linear growth curve model. Calcutta Statistical Association Bulletin 46, 211–229.MathSciNetzbMATHGoogle Scholar
  9. Mandai, N. K., Shah, K. R. and Sinha, Bikas K. (2000). de la Garza phenomenon re-visited. Unpublished Manuscript.Google Scholar
  10. Pázman, A. (1986). Foundations of optimum experimental design. Reidel, Dordrecht.zbMATHGoogle Scholar
  11. Pukelsheim, F. (1993). Optimal design of experiments. Wiley, New York.zbMATHGoogle 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