TayappMG

An auxiliary function to calculate the values for the
Taylor-based Monte-Carlo-approximation for multiple groups. After receiving
some auxiliary matrices and data, the Monte-Carlo observations are generated
and different parts of the final sum are defined. Based on this a number of
the Taylor-based ATS are calculated, where the number can be chosen.

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

TayappMG function

<dl><dt>repetitions</dt>
<dd>a number specifying the number of runs for the
approximation</dd>
<dt>C</dt>
<dd>the used hypothesis matrix</dd>
<dt>MSrootStUpsi</dt>
<dd>the matrix root of the covariance matrix for the Taylor
observations</dd>
<dt>CorData</dt>
<dd>the calculated correlation matrix</dd>
<dt>MvrH</dt>
<dd>an auxiliary matrix for the transformation from vectorized
covariances to vectorized correlations</dd>
<dt>Trace</dt>
<dd>a trace used in the ATS for the test statistic</dd>
<dt>M4</dt>
<dd>an auxiliary matrix for the transformation from vectorized
covariances to vectorized correlations</dd>
<dt>L</dt>
<dd>an auxiliary matrix for the transformation from vectorized
covariances to vectorized correlations</dd>
<dt>P</dt>
<dd>an auxiliary matrix for the transformation from vectorized
covariances to vectorized correlations</dd>
<dt>Q</dt>
<dd>an auxiliary matrix for the transformation from vectorized
covariances to vectorized correlations</dd>
<dt>nv</dt>
<dd>vector of sample sizes</dd></dl>

Arguments

Function for the Taylor-based Monte-Carlo-approximation for multiple groups — TayappMG

<dl>

<dt>repetitions</dt>
<dd>a number specifying the number of runs for the
approximation</dd>


<dt>C</dt>
<dd>the used hypothesis matrix</dd>


<dt>MSrootStUpsi</dt>
<dd>the matrix root of the covariance matrix for the Taylor
observations</dd>


<dt>CorData</dt>
<dd>the calculated correlation matrix</dd>


<dt>MvrH</dt>
<dd>an auxiliary matrix for the transformation from vectorized
covariances to vectorized correlations</dd>


<dt>Trace</dt>
<dd>a trace used in the ATS for the test statistic</dd>


<dt>M4</dt>
<dd>an auxiliary matrix for the transformation from vectorized
covariances to vectorized correlations</dd>


<dt>L</dt>
<dd>an auxiliary matrix for the transformation from vectorized
covariances to vectorized correlations</dd>


<dt>P</dt>
<dd>an auxiliary matrix for the transformation from vectorized
covariances to vectorized correlations</dd>


<dt>Q</dt>
<dd>an auxiliary matrix for the transformation from vectorized
covariances to vectorized correlations</dd>


<dt>nv</dt>
<dd>vector of sample sizes</dd>

</dl>

TayappMG: Function for the Taylor-based Monte-Carlo-approximation for multiple groups

Description

Usage

Value

Arguments