An implementation of data analysis tools for samples of symmetric or Hermitian positive definite matrices, such as collections of covariance matrices or spectral density matrices. The tools in this package can be used to perform: (i) intrinsic wavelet transforms for curves (1D) or surfaces (2D) of Hermitian positive definite matrices with applications to dimension reduction, denoising and clustering in the space of Hermitian positive definite matrices; and (ii) exploratory data analysis and inference for samples of positive definite matrices by means of intrinsic data depth functions and rank-based hypothesis tests in the space of Hermitian positive definite matrices.
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 2017) 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 2017) 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 ([email protected]).
Stable CRAN version: install from within R
Current development version: install via
devtools::install_github("JorisChau/pdSpecEst")
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. 2017. “Intrinsic Data Depth for Hermitian Positive Definite Matrices.” ArXiv Preprint 1706.08289. https://arxiv.org/abs/1706.08289.
Chau, J., and R. von Sachs. 2017. “Intrinsic Wavelet Regression for Curves of Hermitian Positive Definite Matrices.” ArXiv Preprint 1701.03314. https://arxiv.org/abs/1701.03314.
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.
pdkMeansrExamples1D and rExamples2DpdMedianpdSpecClust1D, pdSpecClust2D, pdDepth, pdSpecEst1D, pdSpecEst2D, rExamples1D, rExamples2D, InvWavTransf1D, InvWavTransf2D, pdDist,
pdMean, pdMedian, pdPgram, pdPgram2D, pdNeville, WavTransf1D, WavTransf2D,
pdParTrans, Expm, LogmpdSpecEst1D and pdSpecClust1D based on various new metricspdSpecEst2D and pdSpecClust2DpdPgram2DpdCARTpdConfInt1DH.coeff, InvWavTransf1D, InvWavTransf2D, ParTrans, pdCART, pdConfInt1D, pdDepth, pdMean, pdNeville, pdPgram2D, pdPolynomial,
pdRankTests, pdSpecClust1D, pdSpecClust2D, pdSpecEst1D, pdSpecEst2D, pdSplineReg, rExamples, rExamples2D, WavTransf1D, WavTransf2DpdDist, pdDepth, pdRankTests