Jacobian

A function which calculates the Jacobian matrix for a given
transformation function <code>subdiagonal_mean_ratio_cor</code> or
<code>subdiagonal_mean_ratio_fct</code>

internal

A compilation of tests for hypotheses regarding covariance
and correlation matrices for one or more groups. The hypothesis can
be specified through a corresponding hypothesis matrix and a vector or
by choosing one of the basic hypotheses, while for the structure test,
only the latter works. Thereby Monte-Carlo and Bootstrap-techniques
are used, and the respective method must be chosen, and the functions
provide p-values and mostly also estimators of calculated covariance
matrices of test statistics. For more details on the methodology, see
Sattler et al. (2022) <doi:10.1016/j.jspi.2021.12.001>,
Sattler and Pauly (2024) <doi:10.1007/s11749-023-00906-6>, and
Sattler and Dobler (2025) <doi:10.48550/arXiv.2310.11799>.

Svenja Jedhoff

CovCorTest

Statistical Tests for Covariance and Correlation Matrices and
their Structures

Paavo Sattler

Markus Pauly

Arne C Bathke

Dennis Dobler

Jacobian function

<dl><dt>X</dt>
<dd>vectorized covariance matrix for which the Jacobian matrix is
applied</dd>
<dt>a</dt>
<dd>vector containing the indices which belong to the diagonal of the
covariance matrix</dd>
<dt>d</dt>
<dd>dimension of the covariance matrix</dd>
<dt>p</dt>
<dd>dimension of the vectorized matrix</dd>
<dt>fun</dt>
<dd>transformation function, that should be used.
<code>subdiagonal_mean_ratio_fct</code> or
<code>subdiagonal_mean_ratio_cor</code></dd></dl>

Arguments

Jacobian matrix for transformation functions — Jacobian

<dl>

<dt>X</dt>
<dd>vectorized covariance matrix for which the Jacobian matrix is
applied</dd>


<dt>a</dt>
<dd>vector containing the indices which belong to the diagonal of the
covariance matrix</dd>


<dt>d</dt>
<dd>dimension of the covariance matrix</dd>


<dt>p</dt>
<dd>dimension of the vectorized matrix</dd>


<dt>fun</dt>
<dd>transformation function, that should be used.
<code>subdiagonal_mean_ratio_fct</code> or
<code>subdiagonal_mean_ratio_cor</code></dd>

</dl>

Jacobian: Jacobian matrix for transformation functions

Description

Usage

Value

Arguments