has_ss1

Compares whether the sum of the squared eigenvalues of the supplied symmetric matrices match each other using the property that the sum of the squared eigenvalues of <code>Y</code> equals the trace of <code>Y %*% Y</code>.

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

has_ss1 function

<dl><dt>x</dt>
<dd>A sample or multiple samples of matrices suitable for <code>as_flat()</code>.</dd>
<dt>tolerance</dt>
<dd>Tolerance on the relative difference, passed to <code><a href="/link/all.equal()?package=TFORGE&version=0.1.16" data-mini-rdoc="TFORGE::all.equal()">all.equal()</a></code></dd></dl>

Arguments

Check whether the supplied sample(s) have equal sum of squared eigenvalues — has_ss1

<dl>

<dt>x</dt>
<dd>A sample or multiple samples of matrices suitable for <code>as_flat()</code>.</dd>


<dt>tolerance</dt>
<dd>Tolerance on the relative difference, passed to <code><a href='https://rdrr.io/r/base/all.equal.html'>all.equal()</a></code></dd>

</dl>

has_ss1: Check whether the supplied sample(s) have equal sum of squared eigenvalues

Description

Usage

Value

Arguments