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Ascent with quadratic assistance for the construction of exact experimental designs

Author

Listed:
  • Lenka Filová

    (Comenius University in Bratislava)

  • Radoslav Harman

    (Comenius University in Bratislava
    Johannes Kepler University Linz)

Abstract

In the area of statistical planning, there is a large body of theoretical knowledge and computational experience concerning so-called optimal approximate designs of experiments. However, for an approximate design to be realizable, it must be converted into an exact, i.e., integer, design, which is usually done via rounding procedures. Although rapid, rounding procedures often yield worse exact designs than heuristics that do not require approximate designs at all. In this paper, we build on an alternative principle of utilizing optimal approximate designs for the computation of optimal, or nearly-optimal, exact designs. The principle, which we call ascent with quadratic assistance (AQuA), is an integer programming method based on the quadratic approximation of the design criterion in the neighborhood of the optimal approximate information matrix. To this end, we present quadratic approximations of all Kiefer’s criteria with an integer parameter, including D- and A-optimality and, by a model transformation, I-optimality. Importantly, we prove a low-rank property of the associated quadratic forms, which enables us to use AQuA efficiently and apply it to large design spaces. We numerically demonstrate the robustness and superior performance of the proposed method for selected statistical models under various types of experimental constraints. We also show how can iterative application of AQuA be used for a stratified information-based subsampling of large datasets under a lower bound on the quality and an upper bound on the cost of the subsample.

Suggested Citation

  • Lenka Filová & Radoslav Harman, 2020. "Ascent with quadratic assistance for the construction of exact experimental designs," Computational Statistics, Springer, vol. 35(2), pages 775-801, June.
  • Handle: RePEc:spr:compst:v:35:y:2020:i:2:d:10.1007_s00180-020-00961-9
    DOI: 10.1007/s00180-020-00961-9
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    References listed on IDEAS

    as
    1. Harman, Radoslav & Filová, Lenka, 2014. "Computing efficient exact designs of experiments using integer quadratic programming," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1159-1167.
    2. HaiYing Wang & Min Yang & John Stufken, 2019. "Information-Based Optimal Subdata Selection for Big Data Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 393-405, January.
    3. Peter Goos & Bradley Jones & Utami Syafitri, 2016. "I-Optimal Design of Mixture Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 899-911, April.
    4. Liu, Shuangzhe & Neudecker, Heinz, 1995. "A V-optimal design for Scheffé's polynomial model," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 253-258, May.
    5. Radoslav Harman & Alena Bachratá & Lenka Filová, 2016. "Construction of efficient experimental designs under multiple resource constraints," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(1), pages 3-17, January.
    6. Min Yang & Stefanie Biedermann & Elina Tang, 2013. "On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1411-1420, December.
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    Cited by:

    1. Belmiro P. M. Duarte, 2023. "Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming," Mathematics, MDPI, vol. 11(4), pages 1-17, February.

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