正交表的广义分解
Generalized resolution for orthogonal arrays
摘要：
正交阵列的广义字长模式允许根据广义最小像差准则对正交阵列进行排序（Xu和Wu [Ann. Statist. 29（2001）1066-1077]）。我们提供了一个统计解释的最短的字的正交数组的总和$R^2$值（基于正交编码）或平方典型相关（基于任意编码）的总和。与这些结果直接相关，我们得到了定性因子的两种形式的广义归结，这两种形式都是邓和唐的广义归结的推广。Sinica 9（1999）1071-1082]和Tang and Deng [Ann. Statist. 27（1999）1914-1926]。我们提供了一个充分条件，这些达到其上界，我们提供了明确的上界两类对称设计。按因子概化的分辨率值提供了有用的附加详细信息。
英文摘要：
The generalized word length pattern of an orthogonal array allows a ranking of orthogonal arrays in terms of the generalized minimum aberration criterion (Xu and Wu [Ann. Statist. 29 (2001) 1066-1077]). We provide a statistical interpretation for the number of shortest words of an orthogonal array in terms of sums of $R^2$ values (based on orthogonal coding) or sums of squared canonical correlations (based on arbitrary coding). Directly related to these results, we derive two versions of generalized resolution for qualitative factors, both of which are generalizations of the generalized resolution by Deng and Tang [Statist. Sinica 9 (1999) 1071-1082] and Tang and Deng [Ann. Statist. 27 (1999) 1914-1926]. We provide a sufficient condition for one of these to attain its upper bound, and we provide explicit upper bounds for two classes of symmetric designs. Factor-wise generalized resolution values provide useful additional detail.
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