conf_ss1fixedtrace

conf_ss1fixedtrace_inregion

When a 3x3 symmetric matrix has a trace of zero and the sum of squared eigenvalues is one, then the eigenvalues of the matrix lie on a circle in 3D space.
Under these situations, this function calculates a confidence region (i.e. an interval) for the eigenvalues of the population's extrinsic mean.
The function <code>conf_ss1fixedtrace_inregion()</code> returns whether a set of eigenvalues is inside a confidence region returned by <code>conf_fixedtrace()</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

conf_ss1fixedtrace function

<dl><dt>x</dt>
<dd>A single sample of 3x3 symmetric matrices. <code>x</code> must be either an <code>fsm</code> object or something that <code>as_fsm()</code> can parse.</dd>
<dt>alpha</dt>
<dd>Desired significance level of the approximate confidence region.</dd>
<dt>B</dt>
<dd>Number of bootstrap resamples.</dd>
<dt>check</dt>
<dd>If <code>TRUE</code>, then the extrinsic means of 100 new resamples will be used to check the coverage of the region.</dd>
<dt>evals</dt>
<dd>A set of eigenvalues with trace of zero and sum of squares of one.</dd>
<dt>cr</dt>
<dd>A confidence region returned by <code>conf_ss1fixedtrace()</code>.</dd></dl>

Arguments

Eigenvalue confidence interval under trace=0 and sum of square constraint — conf_ss1fixedtrace

<dl>

<dt>x</dt>
<dd>A single sample of 3x3 symmetric matrices. <code>x</code> must be either an <code>fsm</code> object or something that <code>as_fsm()</code> can parse.</dd>


<dt>alpha</dt>
<dd>Desired significance level of the approximate confidence region.</dd>


<dt>B</dt>
<dd>Number of bootstrap resamples.</dd>


<dt>check</dt>
<dd>If <code>TRUE</code>, then the extrinsic means of 100 new resamples will be used to check the coverage of the region.</dd>


<dt>evals</dt>
<dd>A set of eigenvalues with trace of zero and sum of squares of one.</dd>


<dt>cr</dt>
<dd>A confidence region returned by <code>conf_ss1fixedtrace()</code>.</dd>

</dl>

conf_ss1fixedtrace: Eigenvalue confidence interval under trace=0 and sum of square constraint

Description

Usage

Value

Arguments