摘要
In design theory, the alias structure of regular fractional factorial designs is elegantly described with group theory. However, this approach cannot be applied to nonregular designs directly. For an arbitrary nonregular design, a natural question is how to describe the confounding relations between its effects, is there any inner structure similar to regular designs？ The aim of this article is to answer this basic question. Using coefficients of indicator function, confounding structure of nonregular fractional factorial designs is obtained as linear constrains on the values of effects. A method to estimate the sparse significant effects in an arbitrary nonregular design is given through an example.
In design theory, the alias structure of regular fractional factorial designs is elegantly described with group theory. However, this approach cannot be applied to nonregular designs directly. For an arbitrary nonregular design, a natural question is how to describe the confounding relations between its effects, is there any inner structure similar to regular designs？ The aim of this article is to answer this basic question. Using coefficients of indicator function, confounding structure of nonregular fractional factorial designs is obtained as linear constrains on the values of effects. A method to estimate the sparse significant effects in an arbitrary nonregular design is given through an example.
基金
supported by the NNSF of China grant 71161013
the MOE Project of Humanities and Social Sciences No.10YGC630203
