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We present some optimal criteria to evaluate model-robustness of non-regular two-level fractional factorial designs. Our method is based on minimizing the sum of squares of all the off-diagonal elements in the information matrix, and considering expectation under appropriate distribution functions for unknown contamination of the interaction effects. By considering uniform distributions on symmetric support, our criteria can be expressed as linear combinations of $B_s(d)$ characteristic, which is used to characterize the generalized minimum aberration. We give some empirical studies for 12-run non-regular designs to evaluate our method.
It is known that a Markov basis of the binary graph model of a graph $G$ corresponds to a set of binomial generators of cut ideals $I_{widehat{G}}$ of the suspension $widehat{G}$ of $G$. In this paper, we give another application of cut ideals to sta
A new class of two-level non-regular fractional factorial designs is defined. We call this class an {it affinely full-dimensional factorial design}, meaning that design points in the design of this class are not contained in any affine hyperplane in
The minimum aberration criterion has been frequently used in the selection of fractional factorial designs with nominal factors. For designs with quantitative factors, however, level permutation of factors could alter their geometrical structures and
The highly influential two-group model in testing a large number of statistical hypotheses assumes that the test statistics are drawn independently from a mixture of a high probability null distribution and a low probability alternative. Optimal cont
Optimal two-treatment, $p$ period crossover designs for binary responses are determined. The optimal designs are obtained by minimizing the variance of the treatment contrast estimator over all possible allocations of $n$ subjects to $2^p$ possible t