论文标题
方差分析用于度量空间中的数据，并应用于空间点模式
ANOVA for Data in Metric Spaces, with Applications to Spatial Point Patterns
论文作者
论文摘要
我们对基于度量空间中数据测试组差异的最新类似方差分析的程序进行了回顾，并提出了新的此类程序。我们的统计数据基于经典的莱文检测到分散差异的测试。它仅使用数据点的成对距离，并且可以在数据空间中的barycenters（“广义含义”）计算的情况下快速，精确地计算得很慢，仅通过近似甚至是不可行的。我们显示了测试统计量的渐近正态性和为空间点模式数据进行的仿真研究，其中我们比较了1路ANOVA设置中的各种过程。作为应用程序，我们在矿物浮选过程中对气泡的数据集执行2条方差分析。
We give a review of recent ANOVA-like procedures for testing group differences based on data in a metric space and present a new such procedure. Our statistic is based on the classic Levene's test for detecting differences in dispersion. It uses only pairwise distances of data points and and can be computed quickly and precisely in situations where the computation of barycenters ("generalized means") in the data space is slow, only by approximation or even infeasible. We show the asymptotic normality of our test statistic and present simulation studies for spatial point pattern data, in which we compare the various procedures in a 1-way ANOVA setting. As an application, we perform a 2-way ANOVA on a data set of bubbles in a mineral flotation process.
