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For a particular experimental design, there is interest in finding whichpolynomial models can be identified in the usual regression set up. Thealgebraic methods based on Groebner bases provide a systematic way of doingthis. The algebraic method does not in general produce all estimable models butit can be shown that it yields models which have minimal average degree in awell-defined sense and in both a weighted and unweighted version. This providesan alternative measure to that based on "aberration" and moreover is applicableto any experimental design. A simple algorithm is given and bounds are derivedfor the criteria, which may be used to give asymptotic Nyquist-likeestimability rates as model and sample sizes increase.

Minimal average degree aberration and the state polytope for experimental designs