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

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Stochastic Models, Statistics and Their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((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.

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Notes

  1. 1.

    If 𝒞(A)⊆𝒞(M), then A T M − A does not depend on the choice of the generalized inverse of M.

References

  1. Atkinson AC, Donev AN (1996) Experimental designs optimally balanced for trend. Technometrics 38(4):333–341

    Article  MathSciNet  MATH  Google Scholar 

  2. Atkinson AC, Donev AN, Tobias RD (2007) Optimum experimental designs, with SAS. Oxford University Press, New York

    Google Scholar 

  3. Cook D, Fedorov V (1995) Constrained optimization of experimental design. Statistics 26(2):129–148

    Article  MathSciNet  MATH  Google Scholar 

  4. Cox DR (1951) Some systematic experimental designs. Biometrika 38(3/4):312–323

    Article  MathSciNet  MATH  Google Scholar 

  5. Joshi S, Boyd S (2009) Sensor selection via convex optimization. IEEE Trans Signal Process 57(2):451–462

    Article  MathSciNet  Google Scholar 

  6. Pázman A (1986) Foundations of optimum experimental design. Reidel, Dordrecht

    MATH  Google Scholar 

  7. Papp D (2012) Optimal designs for rational function regression. J Am Stat Assoc 107(497):400–411

    Article  MathSciNet  MATH  Google Scholar 

  8. Pukelsheim F (2006) Optimal design of experiments. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  9. Tack L, Vandebroek M (2001) (𝒟 t ,c)-optimal run orders. J Stat Plan Inference 98(1-2):293–310

    Article  MathSciNet  MATH  Google Scholar 

  10. Sagnol G (2012) Picos, a python interface to conic optimization solvers. Technical report 12-48. ZIB: http://picos.zib.de

  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

    Article  MATH  Google Scholar 

  12. Vandenberghe L (2010) The CVXOPT linear and quadratic cone program solvers. http://cvxopt.org/documentation/coneprog.pdf

  13. Vandenberghe L, Boyd S, Wu SP (1998) Determinant maximization with linear matrix inequality constraints. SIAM J Matrix Anal Appl 19(2):499–533

    Article  MathSciNet  MATH  Google Scholar 

  14. Welch WJ (1982) Branch-and-bound search for experimental designs based on D-optimality and other criteria. Technometrics 24(1):41–48

    MathSciNet  MATH  Google Scholar 

  15. Yu Y (2010) Monotonic convergence of a general algorithm for computing optimal designs. Ann Stat 38(3):1593–1606

    Article  Google Scholar 

Download references

Acknowledgements

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

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Authors and Affiliations

  1. Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 84248, Bratislava, Slovakia

    Radoslav Harman

  2. Dept. Optimization, Zuse Institut Berlin, Takustr. 7, 14195, Berlin, Germany

    Guillaume Sagnol

Authors
  1. Radoslav Harman
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  2. Guillaume Sagnol
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Corresponding author

Correspondence to Radoslav Harman .

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Editors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Ansgar Steland

  2. Dept. of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wrocław, Poland

    Ewaryst Rafajłowicz

  3. Inst. of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, Poland

    Krzysztof Szajowski

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Harman, R., Sagnol, G. (2015). Computing D-Optimal Experimental Designs for Estimating Treatment Contrasts Under the Presence of a Nuisance Time Trend. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_10

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