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Uniform designs limit aliasing

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  • Fred J. Hickernell

Abstract

When fitting a linear regression model to data, aliasing can adversely affect the estimates of the model coefficients and the decision of whether or not a term is significant. Optimal experimental designs give efficient estimators assuming that the true form of the model is known, while robust experimental designs guard against inaccurate estimates caused by model misspecification. Although it is rare for a single design to be both maximally efficient and robust, it is shown here that uniform designs limit the effects of aliasing to yield reasonable efficiency and robustness together. Aberration and resolution measure how well fractional factorial designs guard against the effects of aliasing. Here it is shown that the definitions of aberration and resolution may be generalised to other types of design using the discrepancy. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Fred J. Hickernell, 2002. "Uniform designs limit aliasing," Biometrika, Biometrika Trust, vol. 89(4), pages 893-904, December.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:4:p:893-904
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    Citations

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    Cited by:

    1. Yu, Jun & Meng, Xiran & Wang, Yaping, 2023. "Optimal designs for semi-parametric dose-response models under random contamination," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    2. Biao Luo & Hongyi Li & Yingying Wei & Zujun Ou, 2022. "Uniform design with prior information of factors under weighted wrap-around $$L_2$$ L 2 -discrepancy," Computational Statistics, Springer, vol. 37(5), pages 2717-2739, November.
    3. Chatterjee, Kashinath & Qin, Hong, 2008. "A new look at discrete discrepancy," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2988-2991, December.
    4. Hong Qin & Na Zou & Kashinath Chatterjee, 2009. "Connection between uniformity and minimum moment aberration," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 79-88, June.
    5. Fang Pang & Min-Qian Liu, 2012. "A note on connections among criteria for asymmetrical factorials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 23-32, January.
    6. Zou, Na & Ren, Ping & Qin, Hong, 2009. "A note on Lee discrepancy," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 496-500, February.
    7. Li, Peng-Fei & Chen, Bao-Jiang & Liu, Min-Qian & Zhang, Run-Chu, 2006. "A note on minimum aberration and clear criteria," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1007-1011, May.
    8. Bochuan Jiang & Fei Wang & Yaping Wang, 2022. "Construction of uniform mixed-level designs through level permutations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 753-770, August.
    9. Li, Peng-Fei & Liu, Min-Qian & Zhang, Run-Chu, 2004. "Some theory and the construction of mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 105-116, August.
    10. Chen, Jie & Liu, Min-Qian, 2008. "Optimal mixed-level supersaturated design with general number of runs," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2496-2502, October.
    11. Qiming Bai & Hongyi Li & Shixian Zhang & Jiezhong Tian, 2023. "Design Efficiency of the Asymmetric Minimum Projection Uniform Designs," Mathematics, MDPI, vol. 11(3), pages 1-20, February.
    12. Mingyao Ai & Shuyuan He, 2006. "Interaction balance for symmetrical factorial designs with generalized minimum aberration," Statistical Papers, Springer, vol. 47(1), pages 125-135, January.
    13. E. Androulakis & C. Koukouvinos, 2013. "A new variable selection method for uniform designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2564-2578, December.
    14. Yang, Xue & Chen, Hao & Liu, Min-Qian, 2014. "Resolvable orthogonal array-based uniform sliced Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 108-115.
    15. Kang Wang & Zujun Ou & Jiaqi Liu & Hongyi Li, 2021. "Uniformity pattern of q-level factorials under mixture discrepancy," Statistical Papers, Springer, vol. 62(4), pages 1777-1793, August.
    16. Narayanaswamy Balakrishnan & Hong Qin & Kashinath Chatterjee, 2016. "Generalized projection discrepancy and its applications in experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 19-35, January.
    17. Rong-Xian Yue & Kashinath Chatterjee, 2010. "Bayesian U-type design for nonparametric response surface prediction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 219-231, September.
    18. A. M. Elsawah & Kai-Tai Fang & Ping He & Hong Qin, 2021. "Sharp lower bounds of various uniformity criteria for constructing uniform designs," Statistical Papers, Springer, vol. 62(3), pages 1461-1482, June.
    19. Li, Hongyi & Chatterjee, Kashinath & Li, Bo & Qin, Hong, 2016. "Construction of Sudoku-based uniform designs with mixed levels," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 111-118.
    20. Yang Huang & Yongdao Zhou, 2022. "Convergence of Uniformity Criteria and the Application in Numerical Integration," Mathematics, MDPI, vol. 10(19), pages 1-20, October.
    21. Hong Qin & Mingyao Ai, 2007. "A note on the connection between uniformity and generalized minimum aberration," Statistical Papers, Springer, vol. 48(3), pages 491-502, September.
    22. Yong-Dao Zhou & Kai-Tai Fang, 2013. "An efficient method for constructing uniform designs with large size," Computational Statistics, Springer, vol. 28(3), pages 1319-1331, June.
    23. Fasheng Sun & Jie Chen & Min-Qian Liu, 2011. "Connections between uniformity and aberration in general multi-level factorials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 305-315, May.

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