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Journal of Statistical Theory and Practice

, Volume 7, Issue 4, pp 732–744 | Cite as

On the Connectivity Problem for m-Way Designs

Article

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.

Keywords

Adjusted orthogonality Connectivity Estimability Information matrix Kernel space Segregated component space 

AMS Subject Classification

62K99 62K10 

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Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of SurreyGuildfordUK

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