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Mathematics > Statistics Theory

arXiv:2012.11478 (math)
[Submitted on 21 Dec 2020]

Title:Optimality of multi-way designs

Authors:Sunanda Bagchi, Bhaskar Bagchi
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Abstract:In this paper we study optimality aspects of a certain type of designs in a multi-way heterogeneity setting. These are ``duals" of plans orthogonal through the block factor (POTB). Here by the dual of a main effect plan (say $\rho$) we mean a design in a multi-way heterogeneity setting obtained from $\rho$ by interchanging the roles of the block factors and the treatment factors. Specifically, we take up two series of universally optimal POTBs for symmetrical experiments constructed in Morgan and Uddin (1996). We show that the duals of these plans, as multi-way designs, satisfy M-optimality.
Next, we construct another series of multiway designs and proved their M-optimality, thereby generalising the result of Bagchi and Shah (1989). It may be noted that M-optimality includes all commonly used optimality criteria like A-, D- and E-optimality.
Subjects: Statistics Theory (math.ST)
MSC classes: 62k05
Cite as: arXiv:2012.11478 [math.ST]
  (or arXiv:2012.11478v1 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2012.11478

Submission history

From: Sunanda Bagchi [view email]
[v1] Mon, 21 Dec 2020 16:47:42 UTC (22 KB)
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