Regular fractions of factorial arrays

Ulrike Groemping, Rosemary Anne Bailey

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


For symmetric arrays of two-level factors, a regular fraction is a well-defined concept, which has been generalized in various ways to arrays of s-level factors with s a prime or prime power, and also to mixed-level arrays with arbitrary numbers of factor levels. This paper introduces three further definitions of a regular fraction for a general array, based on squared canonical correlations or the commuting of projectors. All classical regularity definitions imply regularity under the new definitions, which also permit further arrays to be considered regular. As a particularly natural example, non-cyclic Latin squares, which are not regular under several classical regularity definitions, are regular fractions under the proposed definitions. This and further examples illustrate the different regularity concepts.
Original languageEnglish
Title of host publicationmODa 11---Advances in Model-Oriented Design and Analysis
Subtitle of host publicationProceedings of the 11th International Workshop in Model-Oriented Design and Analysis
EditorsJoachim Kunert, Christine H. M"uller, Anthony C. Atkinson
Number of pages9
ISBN (Electronic)978-3-319-31266-8
ISBN (Print)978-3-319-31264-4
Publication statusPublished - 2016

Publication series

NameContributions to Statistics


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