标题： 组合数据集中的公共子空间检验与结构零 显示英文标题

标题： Testing for a common subspace in compositional datasets with structural zeros

摘要： 在处理组成数据集的实际应用中，很容易遇到结构零的存在。后者出现在由于物理限制，某些变量在研究的人群子集内本质上为零的情况下。经典的Aitchison方法要求组成成分的所有成分严格为正，因为最常用的统计技术适应到组成框架上依赖于计算这些成分的对数比。因此，包含结构零的数据集通常被分为两个子集，一个包含具有结构零的观测值，另一个包含所有其他数据。然后分别对这两个子集进行统计分析，假设这两个数据集来自两个不同的子种群。然而，当将总体分成两个子种群仅仅是人为的时候，这种方法可能导致结果不完整。为了克服这一限制并提高这种方法的稳健性，我们引入了一个统计检验，以检查两个数据集的前K个主成分是否生成相同的向量空间。当数据在单纯形上服从正态分布时，通过解析方法推导出相应的零分布近似值，在其他情况下则通过非参数引导方法进行。模拟数据的结果表明，所提出的过程可以区分子种群共享共同子空间的情况与实际不同的情况。所提出的方法性能也在一个关于微生物组测量的实验数据集上进行了测试。 显示英文摘要

摘要： In real world applications dealing with compositional datasets, it is easy to face the presence of structural zeros. The latter arise when, due to physical limitations, one or more variables are intrinsically zero for a subset of the population under study. The classical Aitchison approach requires all the components of a composition to be strictly positive, since the adaptation of the most widely used statistical techniques to the compositional framework relies on computing the logratios of these components. Therefore, datasets containing structural zeros are usually split in two subsets, the one containing the observations with structural zeros and the one containing all the other data. Then statistical analysis is performed on the two subsets separately, assuming the two datasets are drawn from two different subpopulations. However, this approach may lead to incomplete results when the split into two populations is merely artificial. To overcome this limitation and increase the robustness of such an approach, we introduce a statistical test to check whether the first K principal components of the two datasets generate the same vector space. An approximation of the corresponding null distribution is derived analytically when data are normally distributed on the simplex and through a nonparametric bootstrap approach in the other cases. Results from simulated data demonstrate that the proposed procedure can discriminate scenarios where the subpopulations share a common subspace from those where they are actually distinct. The performance of the proposed method is also tested on an experimental dataset concerning microbiome measurements.