Bootstrap_trans

This function generates n1 normal distributed random vectors
with covariance matrix HatCov, which matrix root MSrootHatCov is given and
expectation vector vX. For the generated bootstrap sample the value of the
ATS based on a transformation is calculated

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

Bootstrap_trans function

<dl><dt>N.sim</dt>
<dd>control variable for using sapply</dd>
<dt>n1</dt>
<dd>a scalar, declaring the sample size for the bootstrap sample</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>C</dt>
<dd>a hypothesis matrix for calculating the ATS</dd>
<dt>MSrootHatCov</dt>
<dd>matrix root of the covariance matrix HatCov, to generate
the bootstrap sample</dd>
<dt>vX</dt>
<dd>the expectation vector for the bootstrap sample</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

Bootstrap using transformation for one group — Bootstrap_trans

<dl>

<dt>N.sim</dt>
<dd>control variable for using sapply</dd>


<dt>n1</dt>
<dd>a scalar, declaring the sample size for the bootstrap sample</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>C</dt>
<dd>a hypothesis matrix for calculating the ATS</dd>


<dt>MSrootHatCov</dt>
<dd>matrix root of the covariance matrix HatCov, to generate
the bootstrap sample</dd>


<dt>vX</dt>
<dd>the expectation vector for the bootstrap sample</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>

Bootstrap_trans: Bootstrap using transformation for one group

Description

Usage

Value

Arguments