HDTD (version 1.6.0)

HDTD-package: Estimation and Hypothesis Testing in High-Dimensional Transposable Data

Description

The package HDTD offers functions to estimate and test the matrix parameters of transposable data in high-dimensional settings.

Details

The term transposable data refers to datasets that are structured in a matrix form such that both the rows and columns correspond to variables of interest. For example, consider microarray studies in genetics where multiple RNA samples across different tissues are available per subject. In this case, a data matrix can be created with row variables the genes, column variables the tissues and measurements the corresponding expression levels.

The function meanmat.hat estimates the mean matrix of the transposable data.

The mean relationship of the row and column variables can be tested using the function meanmat.ts. The implemented test is nonparametric and not seriously restricted by the dependence structure among and/or between the row and column variables.

The function covmat.hat provides Stein-type shrinkage estimators for the row covariance matrix and/or for the column covariance matrix under a matrix-variate normal model.

The sphericity and identity hypothesis for the row or column covariance matrix can be tested using the function covmat.ts. Both tests are nonparametric, i.e., they do not rely on a normality assumption.

There are three utility functions that allow the user to change to interchange the role of row and column variables (transposedata), to center the transposable data (centerdata) or to rearrange the order of the row and/or column variables (orderdata).

References

Touloumis, A., Tavare, S. and Marioni, J.C. (2015). Testing the Mean Matrix in High-Dimensional Transposable Data. Biometrics, 71, 157-166. Touloumis, A., Marioni, J.C. and Tavare, S. (2013). Hypothesis Testing for the Covariance Matrix in High-Dimensional Transposable Data with Kronecker Product Dependence Structure. http://arxiv.org/abs/1404.7684.

Examples

data(VEGFmouse)
## The sample mean matrix.
sample.mean <- meanmat.hat(VEGFmouse,40)
sample.mean
## Testing if there is no tissue effect on the mean expression level for each gene.
tistest <- meanmat.ts(VEGFmouse,40,group.sizes=9,voi="columns")
tistest
# Estimating the covariance matrices of the genes (rows) and of the tissues (columns).
estcovmat <- covmat.hat(VEGFmouse,40,shrink="both",centered=FALSE)
estcovmat
## Hypothesis tests for the covariance matrix of the genes (rows).
genestest <- covmat.ts(VEGFmouse,40,"rows",FALSE)
genestest
## Hypothesis tests for the covariance matrix of the tissues (columns).
tissuestest <- covmat.ts(VEGFmouse,40,"columns",FALSE)
tissuestest