Abstract
We propose a method for selecting terms to be included into a regression model, when a part of the primary candidates is specified (e.g., the main effects), and discuss related experimental design problems. A distinctive feature here is a deficit in the admissible number of experiments in comparison with a much larger number of candidate terms. We apply a large number of random projections of candidate terms to eliminate spurious terms. The design problem is solved for a linear regression with a very large number of interactions.
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Notes
- 1.
The model (1) resembles a model that was proposed by Cook and Weisberg (2004). A fundamental difference is that here s is selected at random and only β is estimated, while in Cook and Weisberg (2004) both β and s are estimated. See Skubalska-Rafajłowicz and Rafajłowicz (2012) for further discussion and references.
- 2.
Strictly speaking, \(\mathbf{M}_{\mathbb{S}}\) is the Fisher information matrix for fixed \(\mathbb{S}\) subject to the hypothesis that \(b_{j}^{0}=0\), j=1,2,…,K.
- 3.
One can consider the Plackett and Burman designs for estimating main effects, but in our opinion they share the same drawback.
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Skubalska-Rafajłowicz, E., Rafajłowicz, E. (2013). Random Projections in Model Selection and Related Experimental Design Problems. In: Ucinski, D., Atkinson, A., Patan, M. (eds) mODa 10 – Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00218-7_27
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