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
发布时间：2018-08-10 17:28
【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.
[Abstract]:This paper studies the equilibrium of basic education resources allocation in Beijing by means of spatial statistical test.Moran's I statistic is commonly used to test the spatial distribution uniformity.But when inferring from Moran's I statistic,people often use asymptotic normal distribution or obtain empirical distribution by Bootstrap repeated sampling. Jin and Lee (2014) show that Bootstrap-based Moran's I statistics satisfy the properties of uniform approximation and asymptotic normality. Similar statistical tools are used to prove that the asymptotic distribution of statistics based on random weighting also satisfies these good properties. The method is applied to the spatial aggregation test of the ratio of teachers to school-age children and the ratio of teachers to school-age children in Beijing elementary education, and the results are compared with those obtained by other test methods. The conclusion shows that under different adjacent concepts (geographic adjacency, policy space adjacency), the conclusion obtained by the method conforms to the common sense.
【作者单位】： 中国人民大学应用统计科学研究中心统计学院;浙江理工大学经济管理学院;
【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)
【分类号】：G639.2;O212.1
，
本文编号：2175672
[Abstract]:This paper studies the equilibrium of basic education resources allocation in Beijing by means of spatial statistical test.Moran's I statistic is commonly used to test the spatial distribution uniformity.But when inferring from Moran's I statistic,people often use asymptotic normal distribution or obtain empirical distribution by Bootstrap repeated sampling. Jin and Lee (2014) show that Bootstrap-based Moran's I statistics satisfy the properties of uniform approximation and asymptotic normality. Similar statistical tools are used to prove that the asymptotic distribution of statistics based on random weighting also satisfies these good properties. The method is applied to the spatial aggregation test of the ratio of teachers to school-age children and the ratio of teachers to school-age children in Beijing elementary education, and the results are compared with those obtained by other test methods. The conclusion shows that under different adjacent concepts (geographic adjacency, policy space adjacency), the conclusion obtained by the method conforms to the common sense.
【作者单位】： 中国人民大学应用统计科学研究中心统计学院;浙江理工大学经济管理学院;
【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)
【分类号】：G639.2;O212.1
，
本文编号：2175672
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