论文标题
高维Manova通过引导及其应用于功能和稀疏计数数据
High-dimensional MANOVA via Bootstrapping and its Application to Functional and Sparse Count Data
论文作者
论文摘要
我们通过引导最大统计量提出了一种新的方法来解决高维多元方差分析的问题，该统计涉及样品平均值矢量的差异。提出的方法是通过构建人口平均向量差异的同时置信区域进行的。它适用于同时测试潜在的两个以上人群的几对平均向量的平等。通过利用在相关应用中自然特征的方差衰减属性，我们能够为高斯近似，自举近似和测试的大小提供无维和几乎参数收敛速率。我们证明了针对功能数据和稀疏计数数据的方差分析问题的建议方法。所提出的方法证明在模拟和几个实际数据应用中效果很好。
We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors. The proposed method proceeds via the construction of simultaneous confidence regions for the differences of population mean vectors. It is suited to simultaneously test the equality of several pairs of mean vectors of potentially more than two populations. By exploiting the variance decay property that is a natural feature in relevant applications, we are able to provide dimension-free and nearly-parametric convergence rates for Gaussian approximation, bootstrap approximation, and the size of the test. We demonstrate the proposed approach with ANOVA problems for functional data and sparse count data. The proposed methodology is shown to work well in simulations and several real data applications.
