Aspects of optimality of plans orthogonal through other factors
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 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 experiments, where is a prime power. The plan is universally optimal.
Keywords
Cite
@article{arxiv.2012.11180,
title = {Aspects of optimality of plans orthogonal through other factors},
author = {Bhaskar Bagchi and Sunanda Bagchi},
journal= {arXiv preprint arXiv:2012.11180},
year = {2020}
}