Nonparametric Bootstrap Inference for the Eigenvalues of Geophysical Tensors
设计了适用于单样本和多样本情境的特征值假设检验方法，允许一般分布和多个样本，并应用于地球物理数据。
Symmetric matrices (tensors) are measured in geophysics and other disciplines, including in medical imaging, and typically their eigenvalues have valuable scientific interpretations. We design pivotal bootstrap hypothesis tests of specified eigenvalues or eigenvalue multiplicities in one-sample situations and for equal eigenvalues in k-sample situations. Our tests are more broadly applicable than existing tests by allowing very general distributions, allowing three or more samples, and accounting for common constraints in geophysical measurements. Simulations indicate that our tests generally perform well and have improved power in situations where there are existing formal hypothesis tests (eigenvalue multiplicity tests and 2-sample tests of unconstrained eigenvalues). We show fast O(n−2) convergence of test size for our pivotal k-sample tests. We also propose confidence regions for eigenvalues and apply our tests to four geophysical data sets. An R package accompanies this article.