离散偏差D(d;γ)及其在试验设计中的应用  

Discrete Discrepancy D(d;γ) and Its Applications in Experimental Designs

作　　者：汪政红[1] 覃红[2] 

机构地区：[1]中南民族大学数学与统计学学院,武汉430074 [2]华中师范大学数学与统计学学院,武汉430079

出　　处：《应用数学学报》2015年第5期944-955,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11271147;11401596;11301546)资助项目

摘　　要：离散偏差D(d;γ)是由Hickernell和Liu提出的并用来评价混水平设计的均匀性的度量.本文探讨了以离散偏差D(d;γ)为度量的均匀性准则与广义最小低阶混杂、正交性准则之间的关系,由此来进一步说明采用离散偏差度量均匀性的合理性.同时,本文利用Kronecker积的性质得到了混水平设计的离散偏差值D(d;γ)的一个下界,并通过一些实例验证了这个下界是可以达到的.The discrete discrepancy D（d;γ） proposed by Hickernell and Liu has been used to measure the uniformity of mixed-level fractional factorial designs.In this paper,we derive links among criteria of uniformity measured by discrete discrepancy D（d;γ）,generalized minimum aberration and orthogonality,which further shows the statistical justification of discrete discrepancy D（d;γ）.We also obtain a lower bound for the discrete discrepancy value of mixed-level fractional factorial design by application of Kronecker calculus for factorial arrangements,and some examples illustrate that this lower bound is tight.

关 键 词：离散偏差 广义最小低阶混杂 均匀性 正交性 下界 

分 类 号：O212.6[理学—概率论与数理统计]