Pivotal bootstrap hypothesis tests for the eigenvalues of geophysical matrices
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: "complex, bootstrap, complex, hypothesis test, matrix-data, tensors
Session: IPS 784 - Statistical Advances Across Diverse Complex Data Landscapes
Wednesday 8 October 2 p.m. - 3:40 p.m. (Europe/Amsterdam)
Abstract
Symmetric matrices (also known as tensors) are measured in geophysics, medical imaging and other disciplines. The eigenvalues of these matrices typically have valuable scientific interpretation. We have developed pivotal bootstrap hypothesis tests for the eigenvalues of the mean matrix. An R software package makes these tools readily accessible and we have used this software for simulations and applications to geophysical data. Our new test for the multiplicities of eigenvalues (of the population mean) performs extremely well compared to the existing test. When sampling from multiple populations, the tests for equality of eigenvalues (of the population means) improve on existing tests when there is large heteroskedasticity, when eigenvalues are nearly degenerate, or when eigenvalues are subject to common constraints in geophysical measurements.