© 1995 by Biometrika Trust
Articles |
Screening by conference designs
1 Physikalisch-Technische Bundesanstalt Abbestr. 2-12, D-10587 Berlin, Germany
2 Institut für Mathematik, Universität Wien Strudlhofgasse 4, A-1090 Wien, Austria
Received for publication 1 December 1993.
Revision received 1 February 1994.
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Abstract |
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Screening experiments aim to identify the relevant variables within some process potentially depending on a large number of variables. In this paper we introduce a new class of experimental designs called edge designs. These designs allow a model-independent estimate of the set of relevant variables, thus providing more robustness than traditional designs. We give a bound on the determinant of the information matrix of certain edge designs, and show that a large class of edge designs meeting this bound can be constructed from conference matrices. We also show that the resulting conference designs have an optimal space exploration property which guards against unexpected nonlinearities. We survey the existence of and constructions for conference matrices, and, for n < 50 variables, give explicit such matrices when n is a prime, and references to explicit constructions otherwise.
Key Words: Conference design • Conference matrix • Edge design • Fractional factorial design • Linear model • Model-independent estimate • Screening experiment • Skew Hadamard matrix