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Mathematics > Statistics Theory

arXiv:2012.11180 (math)
[Submitted on 21 Dec 2020]

Title:Aspects of optimality of plans orthogonal through other factors

Authors:Bhaskar Bagchi, Sunanda Bagchi
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Abstract:The concept of orthogonality through the block factor (OTB), defined in Bagchi (2010), is extended here to orthogonality through a set (say S) of other factors. We discuss the impact of such an orthogonality on the precision of the estimates as well as on the inference procedure. Concentrating on the case when $S$ is of size two, we construct a series of plans in each of which every pair of other factors is orthogonal through a given pair of factors.
Next we concentrate on plans through the block factors (POTB). We construct POTBs for symmetrical experiments with two and three-level factors. The plans for two factors are E-optimal, while those for three-level factors are universally optimal.
Finally, we construct POTBs for $s^t(s+1)$ experiments, where $s \equiv 3 \pmod 4$ is a prime power. The plan is universally optimal.
Subjects: Statistics Theory (math.ST)
MSC classes: 62k10
Cite as: arXiv:2012.11180 [math.ST]
  (or arXiv:2012.11180v1 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2012.11180

Submission history

From: Sunanda Bagchi [view email]
[v1] Mon, 21 Dec 2020 08:41:23 UTC (17 KB)
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