rsymm_norm

rsymm

Simulate symmetric matrices with elements from a multivariate Normal distribution.

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

rsymm_norm function

<dl><dt>n</dt>
<dd>Number of matrices to generate</dd>
<dt>mean</dt>
<dd>A symmetric matrix specifying the mean of the distribution.</dd>
<dt>sigma</dt>
<dd>A covariance matrix for the vectorised lower triangular elements (arranged by <code>vech()</code>) of the symmetric matrix.
It is passed to <code><a href="/link/mvtnorm%3A%3Armvnorm()?package=TFORGE&version=0.1.16" data-mini-rdoc="TFORGE::mvtnorm::rmvnorm()">mvtnorm::rmvnorm()</a></code> without any transformation.</dd></dl>

Arguments

Simulate Symmetric Matrices with Multivariate Normal Elements — rsymm_norm

<dl>

<dt>n</dt>
<dd>Number of matrices to generate</dd>


<dt>mean</dt>
<dd>A symmetric matrix specifying the mean of the distribution.</dd>


<dt>sigma</dt>
<dd>A covariance matrix for the vectorised lower triangular elements (arranged by <code>vech()</code>) of the symmetric matrix.
It is passed to <code><a href='https://rdrr.io/pkg/mvtnorm/man/Mvnorm.html'>mvtnorm::rmvnorm()</a></code> without any transformation.</dd>

</dl>

rsymm_norm: Simulate Symmetric Matrices with Multivariate Normal Elements

Description

Usage

Value

Arguments

Details

Examples