Minimal average degree aberration and the state polytope for experimental designs

For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Gröbner bases provide a systematic way of doing this. The algebraic method does not, in general, produce all estimable models bu...

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Bibliographic Details
Published in:Annals of the Institute of Statistical Mathematics 2010-08, Vol.62 (4), p.673-698
Main Authors: Berstein, Yael, Maruri-Aguilar, Hugo, Onn, Shmuel, Riccomagno, Eva, Wynn, Henry
Format: Article
Language:English
Subjects:
Aberration
Algebra
Algorithms
Asymptotic properties
Design engineering
Economics
Factorial experiments
Finance
Insurance
Management
Mathematical models
Mathematics
Mathematics and Statistics
Polynomials
Polytopes
Regression
Samples
Statistics
Statistics for Business
Studies
Variables
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Summary:For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Gröbner bases provide a systematic way of doing this. The algebraic method does not, in general, produce all estimable models but it can be shown that it yields models which have minimal average degree in a well-defined sense and in both a weighted and unweighted version. This provides an alternative measure to that based on “aberration” and moreover is applicable to any experimental design. A simple algorithm is given and bounds are derived for the criteria, which may be used to give asymptotic Nyquist-like estimability rates as model and sample sizes increase.
ISSN:0020-3157
1572-9052
DOI:10.1007/s10463-010-0291-8