基于随机加权的空间聚集性检验及其在基础教育师资均衡性评价中的应用  

Random Weighting Method for Moran's I test with Application to the Assessment of Balance of Allocation for Fundamental Educational Resources

作　　者：杜子芳[1] 林一楠[1] 尹建鑫[1] 郑冰[2] 

机构地区：[1]中国人民大学应用统计科学研究中心统计学院,北京100872 [2]浙江理工大学经济管理学院,浙江杭州310018

出　　处：《数学的实践与认识》2017年第11期50-65,共16页Mathematics in Practice and Theory

基　　金：北京市教育科学"十二五"规划重点课题(优先关注)"北京教育基本公共服务水平评价研究"(其他)

摘　　要：使用空间统计检验方法研究北京基础教育资源分配的均衡性问题.对于空间分布均匀性的检验,常用的统计量是Moran's I统计量.但基于Moran's I统计量做推断的时候,人们往往用渐进正态分布或者用Bootstrap反复抽样得到经验分布来进行.提出使用随机加权法进行统计量的经验检验.Jin和Lee(2014)文中得出基于Bootstrap的Moran's I统计量满足一致逼近和渐进正态等性质.采用类似的统计工具证明了基于随机加权得到的统计量的渐进分布也满足这些良好性质.填补了用随机加权法在空间统计量的推断中理论保证的空白.通过模拟研究,证明了所提算法的有效性.方法应用于北京基础教育的师资-适龄儿童数比例,师资-在校生数比例的空间聚集性检验中得到了良好的应用,并与其它检验方法所得结论进行比较.结论显示在不同相邻概念(地理相邻、政策空间相邻)下,方法得到的结论符合常理.We study the testing for spatial clustering phenomenon,which has an application in the assessment of balance of allocation for fundamental educational resources.Moran's I statistics is commonly used test statistics for such spatial test purpose.Based on Moran's I,usually asymptotic normality or bootstrap method are employed to do the following inference.We propose to use random weighting method here.Some uniformly approximation and asymptotic normal results for bootstrap method are obtained in Jin and Lee(2014),and we get similar results for random weighting,which fill in the gap.We also examine our algorithm's behavior under finite sample size cases through extensive simulation studies.An application of this method on Beijing's teacher-to-children and teacher-to-student ratios across districts through the whole city exhibits good understanding of the gathering result and non-gathering result under different similarity matrix assumptions.

关 键 词：随机加权法 BOOTSTRAP 空间聚集性检验 Moran’s I 统计量 

分 类 号：G639.2[文化科学—教育学] O212.1[理学—概率论与数理统计]