The pdSpecEst package

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.

The tools in this package can be used to perform:

• Intrinsic wavelet transforms for curves (1D) or 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 papers (Chau and Sachs 2019) and (Chau and Sachs 2018) 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 functions and depth rank-based hypothesis tests. These implementations are based on the paper (Chau, Ombao, and Sachs 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.

Author and maintainer: Joris Chau (joris.chau@openanalytics.eu).

Installation

• Stable CRAN version: install from within R

References

Chau, J. 2018. “Advances in Spectral Analysis for Multivariate, Nonstationary and Replicated Time Series.” PhD thesis, Universite catholique de Louvain.

Chau, J., H. Ombao, and R. von Sachs. 2019. “Intrinsic Data Depth for Hermitian Positive Definite Matrices.” Journal of Computational and Graphical Statistics 28 (2): 427–39. https://doi.org/https://doi.org/10.1080/10618600.2018.1537926.

Chau, J., and R. von Sachs. 2018. “Intrinsic Wavelet Regression for Surfaces of Hermitian Positive Definite Matrices.” ArXiv Preprint 1808.08764. https://arxiv.org/abs/1808.08764.

———. 2019. “Intrinsic Wavelet Regression for Curves of Hermitian Positive Definite Matrices.” Journal of the American Statistical Association. https://doi.org/https://doi.org/10.1080/01621459.2019.1700129.