pdSpecEst {pdSpecEst}

pdSpecEst: An Analysis Toolbox for Hermitian Positive Definite Matrices

Description

The pdSpecEst (positive definite Spectral Estimation) package provides data analysis tools for samples of symmetric or Hermitian positive definite matrices, such as collections of positive definite covariance matrices or spectral density matrices.

Details

The tools in this package can be used to perform:

• Intrinsic wavelet transforms for curves (1D) and surfaces (2D) of Hermitian positive definite matrices, with applications to for instance: dimension reduction, denoising and clustering for curves or surfaces of Hermitian positive definite matrices, such as (time-varying) Fourier spectral density matrices. These implementations are based in part on the paper (Chau and von Sachs 2019) and Chapters 3 and 5 of (Chau 2018).

• Exploratory data analysis and inference for samples of Hermitian positive definite matrices by means of intrinsic data depth and depth rank-based hypothesis tests. These implementations are based on the paper (Chau et al. 2019) and Chapter 4 of (Chau 2018).

For more details and examples on how to use the package see the accompanying vignettes in the vignettes folder. An R-Shiny app to demonstrate and test the implemented functionality in the package is available here.

Author and maintainer: Joris Chau ([e-mail]).

Install the current development version via devtools::install_github("JorisChau/pdSpecEst").

References

Chau J (2018). Advances in Spectral Analysis for Multivariate, Nonstationary and Replicated Time Series. phdthesis, Universite catholique de Louvain.

Chau J, Ombao H, von Sachs R (2019). “Intrinsic data depth for Hermitian positive definite matrices.” Journal of Computational and Graphical Statistics, 28(2), 427–439. doi: 10.1080/10618600.2018.1537926.

Chau J, von Sachs R (2019). “Intrinsic wavelet regression for curves of Hermitian positive definite matrices.” Journal of the American Statistical Association. doi: 10.1080/01621459.2019.1700129.