Statistical Tests for Covariance and Correlation Matrices and their Structures
ATS for transformed vectors
Anova-Type-statistic
Anova-Type-Statistic with weighted sum
Bootstrap using transformation for one group
Bootstrap for one and multiple groups
CombTest Object
CovTest Object
Diagonal vectorization
Function to generate bootstrap observations
Extend a matrix to full rank using identity columns
Construct hypothesis matrix and vector from linear covariance model st...
Jacobian matrix for transformation functions
Function to transform the data into a list, if there are not already
Print function for CombTest object
Print function for CovTest object
Auxiliary function to calculate the covariance of the vectorized corre...
Root transformation of the vectorized correlation matrix
Transformation of the vectorized covariance matrix by quotients of mea...
Function for the Taylor-based Monte-Carlo-approximation for one group
Function for the Taylor-based Monte-Carlo-approximation for multiple g...
The Taylor-based Monte-Carlo-approximation for a combined test
Combined test for equality of covariance matrices and correlation matr...
Test for structure of data's correlation matrix
Test for Correlation Matrices
Test for structure of data's covariance matrix
Test for Covariance Matrices
Function to calculate dvech(X t(X))
Vectorization of the upper triangular part of the matrix
Function to calculate vech(X t(X))
Weighted direct sums for lists
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>.