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On the Connectivity Problem for m -Way Designs

Godolphin, JD (2013) On the Connectivity Problem for m -Way Designs Journal of Statistical Theory and Practice, 7 (4). pp. 732-744.

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Abstract

The problem of ascertaining conditions that ensure that an m-way design is connected has occupied the attention of research workers for very many years. One of the significant advances, as well as one of the earliest contributions, was provided by the classic work of J. N. Srivastava and D. A. Anderson in 1970, which gives a necessary and sufficient rank condition for an m-way design to be completely connected. In this article it is shown that the class of estimable parametric functions for an individual factor is derived directly from a simple extension of the Srivastava-Anderson result. This takes the form of a necessary and sufficient rank condition that is expressed in terms of the dimension of a segregated component of the kernel of the design matrix. The result has the interesting property that the connectivity status for all of the individual factors can be found simultaneously. Furthermore, it enables the formulation of several general results, which include the specification of conditions on designs exhibiting adjusted orthogonality. A number of examples are given to illustrate these results. © 2013 Copyright Grace Scientific Publishing, LLC.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Godolphin, JDUNSPECIFIEDUNSPECIFIED
Date : 2 October 2013
Identification Number : 10.1080/15598608.2013.782193
Additional Information : This is an Author's Accepted Manuscript of an article published in Journal of Statistical Theory and Practice, 2013 copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/15598608.2013.782193
Depositing User : Symplectic Elements
Date Deposited : 08 Oct 2013 15:41
Last Modified : 02 Apr 2015 01:08
URI: http://epubs.surrey.ac.uk/id/eprint/804063

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