test_multiplicity_OI

Given a sample from a population of symmetric matrices with Gaussian-distributed elements and orthogonally-invariant covariance, corollary 4.3 by schwartzman2008in;textualTFORGE provides a method to test the eigenvalue multiplicity of the mean matrix.
Orthogonally-invariant covariance is a strong assumption and may not be valid; consider using <code>test_multiplicity()</code> if you are unsure.

The eigenvalues of observed symmetric matrices are often of intense scientific interest. This package offers single sample tests for the eigenvalues of the population mean or the eigenvalue-multiplicity of the population mean. For k-samples, this package offers tests for equal eigenvalues between samples. Included is support for matrices with constraints common to geophysical tensors (constant trace, sum of squared eigenvalues, or both) and eigenvectors are usually considered nuisance parameters. Pivotal bootstrap methods enable these tests to have good performance for small samples (n=15 for 3x3 matrices). These methods were developed and studied by Hingee, Scealy and Wood (2026, "Nonparametric bootstrap inference for the eigenvalues of geophysical tensors", accepted by the Journal of American Statistical Association). Also available is a 2-sample test using a Gaussian orthogonal ensemble approximation and an eigenvalue-multiplicity test that assumes orthogonally-invariant covariance.

Kassel Liam Hingee

TFORGE

Tests for Geophysical Eigenvalues

Art B. Owen

Board of Trustees Leland Stanford Junior University

test_multiplicity_OI function

<dl><dt>x</dt>
<dd>A sample of matrices suitable for <code>as_fsm()</code>.</dd>
<dt>mult</dt>
<dd>A vector specifying the eigenvalue multiplicity under the null hypothesis in descending order of eigenvalue size.</dd>
<dt>B</dt>
<dd>Number of bootstrap samples. If <code>B = 'chisq'</code> then a chi-squared calibration is used instead.</dd>
<dt>refbasis</dt>
<dd>Ignored (for compatibility with <code>test_multiplicity()</code>).</dd></dl>

Arguments

Test of eigenvalue multiplicity assuming orthogonally invariant covariance — test_multiplicity_OI

<dl>

<dt>x</dt>
<dd>A sample of matrices suitable for <code>as_fsm()</code>.</dd>


<dt>mult</dt>
<dd>A vector specifying the eigenvalue multiplicity under the null hypothesis in descending order of eigenvalue size.</dd>


<dt>B</dt>
<dd>Number of bootstrap samples. If <code>B = 'chisq'</code> then a chi-squared calibration is used instead.</dd>


<dt>refbasis</dt>
<dd>Ignored (for compatibility with <code>test_multiplicity()</code>).</dd>

</dl>

test_multiplicity_OI: Test of eigenvalue multiplicity assuming orthogonally invariant covariance

Description

Usage

Value

Arguments

Details