基于Bootstrapping的高维MANOVA及其在函数和稀疏计数数据中的应用
High-dimensional MANOVA via Bootstrapping and its Application to Functional and Sparse Count Data
摘要：
提出了一种新的方法，通过Bootstrapping最大统计量，涉及样本均值向量的差异，高维多变量方差分析的问题。所提出的方法的收益，通过建设的同时置信区域的人口平均向量的差异。它适合于同时检验潜在的两个以上总体的几对均值向量的相等性。通过利用方差衰减属性，这是一个自然的功能，在相关的应用程序，我们能够提供无量纲和接近参数的收敛速度高斯近似，自助近似，和测试的大小。我们证明了所提出的方法与方差分析问题的功能数据和稀疏计数数据。所提出的方法在模拟和几个实际数据应用中表现良好。
英文摘要：
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.
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