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General orthogonal designs for parameter estimation of ANOVA models under weighted sum-to-zero constraints

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  • Xiaodi Wang
  • Yingshan Zhang

Abstract

Traditional studies on optimal designs for ANOVA parameter estimation are based on the framework of equal probabilities of appearance for each factor's levels. However, this premise does not hold in a variety of experimental problems, and it is of theoretical and practical interest to investigate optimal designs for parameters with unequal appearing odds. In this paper, we propose a general orthogonal design via matrix image, in which all columns’ matrix images are orthogonal with each other. Our main results show that such designs have A- and E-optimalities on the estimation of ANOVA parameters which have unequal appearing odds. In addition, we develop two simple methods to construct the proposed designs. The optimality of the design is also validated by a simulation study.

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  • Xiaodi Wang & Yingshan Zhang, 2016. "General orthogonal designs for parameter estimation of ANOVA models under weighted sum-to-zero constraints," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(21), pages 6229-6244, November.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:21:p:6229-6244
    DOI: 10.1080/03610926.2014.957860
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    Cited by:

    1. Wang, Xiaodi & Chen, Xueping & Zhang, Yingshan, 2018. "Feasible blocked multi-factor designs of unequal block sizes," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 102-109.

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