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Minimax design criterion for fractional factorial designs

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  • Yue Yin
  • Julie Zhou

Abstract

An A-optimal minimax design criterion is proposed to construct fractional factorial designs, which extends the study of the D-optimal minimax design criterion in Lin and Zhou (Canadian Journal of Statistics 41, 325–340, 2013 ). The resulting A-optimal and D-optimal minimax designs minimize, respectively, the maximum trace and determinant of the mean squared error matrix of the least squares estimator (LSE) of the effects in the linear model. When there is a misspecification of the effects in the model, the LSE is biased and the minimax designs have some control over the bias. Various design properties are investigated for two-level and mixed-level fractional factorial designs. In addition, the relationships among A-optimal, D-optimal, E-optimal, A-optimal minimax and D-optimal minimax designs are explored. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • Yue Yin & Julie Zhou, 2015. "Minimax design criterion for fractional factorial designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 673-685, August.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:4:p:673-685
    DOI: 10.1007/s10463-014-0470-0
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    References listed on IDEAS

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    1. Rahul Mukerjee & Boxin Tang, 2012. "Optimal fractions of two-level factorials under a baseline parameterization," Biometrika, Biometrika Trust, vol. 99(1), pages 71-84.
    2. Boxin Tang & Julie Zhou, 2013. "D-optimal two-level orthogonal arrays for estimating main effects and some specified two-factor interactions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 325-337, April.
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