度量空间中数据的ANOVA及其在空间点模式中的应用
ANOVA for Data in Metric Spaces, with Applications to Spatial Point Patterns
摘要：
我们给最近的方差分析程序测试组的差异的基础上，在度量空间，并提出了一个新的这样的程序。我们的统计是基于经典的Levene检验检测差异的分散。它仅使用数据点的成对距离，并且可以在数据空间中的重心（“广义均值”）计算缓慢，仅通过近似甚至不可行的情况下快速精确地计算。我们展示了我们的检验统计量的渐近正态性，并对空间点模式数据进行了模拟研究，其中我们比较了单因素方差分析设置中的各种程序。作为一个应用，我们在矿物浮选过程中的气泡的数据集上进行了双向方差分析。
英文摘要：
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.
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