Advertisement

Computing D-Optimal Experimental Designs for Estimating Treatment Contrasts Under the Presence of a Nuisance Time Trend

  • Radoslav HarmanEmail author
  • Guillaume Sagnol
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 122)

Abstract

We prove a mathematical programming characterization of approximate partial D-optimality under general linear constraints. We use this characterization with a branch-and-bound method to compute a list of all exact D-optimal designs for estimating a pair of treatment contrasts in the presence of a nuisance time trend up to the size of 24 consecutive trials.

Keywords

Time Trend Moment Matrix List Open Exact Design Good Linear Unbiased Estimator 
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.

Notes

Acknowledgements

The research of the first author was supported by the VEGA 1/0163/13 grant of the Slovak Scientific Grant Agency.

References

  1. 1.
    Atkinson AC, Donev AN (1996) Experimental designs optimally balanced for trend. Technometrics 38(4):333–341 MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Atkinson AC, Donev AN, Tobias RD (2007) Optimum experimental designs, with SAS. Oxford University Press, New York Google Scholar
  3. 3.
    Cook D, Fedorov V (1995) Constrained optimization of experimental design. Statistics 26(2):129–148 MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cox DR (1951) Some systematic experimental designs. Biometrika 38(3/4):312–323 MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Joshi S, Boyd S (2009) Sensor selection via convex optimization. IEEE Trans Signal Process 57(2):451–462 MathSciNetCrossRefGoogle Scholar
  6. 6.
    Pázman A (1986) Foundations of optimum experimental design. Reidel, Dordrecht zbMATHGoogle Scholar
  7. 7.
    Papp D (2012) Optimal designs for rational function regression. J Am Stat Assoc 107(497):400–411 MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Pukelsheim F (2006) Optimal design of experiments. SIAM, Philadelphia CrossRefzbMATHGoogle Scholar
  9. 9.
    Tack L, Vandebroek M (2001) (𝒟t,c)-optimal run orders. J Stat Plan Inference 98(1-2):293–310 MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Sagnol G (2012) Picos, a python interface to conic optimization solvers. Technical report 12-48. ZIB: http://picos.zib.de
  11. 11.
    Uciński D, Patan M (2007) D-optimal design of a monitoring network for parameter estimation of distributed systems. J Glob Optim 39(2):291–322 CrossRefzbMATHGoogle Scholar
  12. 12.
    Vandenberghe L (2010) The CVXOPT linear and quadratic cone program solvers. http://cvxopt.org/documentation/coneprog.pdf
  13. 13.
    Vandenberghe L, Boyd S, Wu SP (1998) Determinant maximization with linear matrix inequality constraints. SIAM J Matrix Anal Appl 19(2):499–533 MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Welch WJ (1982) Branch-and-bound search for experimental designs based on D-optimality and other criteria. Technometrics 24(1):41–48 MathSciNetzbMATHGoogle Scholar
  15. 15.
    Yu Y (2010) Monotonic convergence of a general algorithm for computing optimal designs. Ann Stat 38(3):1593–1606 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics, Physics and InformaticsComenius UniversityBratislavaSlovakia
  2. 2.Dept. OptimizationZuse Institut BerlinBerlinGermany

Personalised recommendations