pdSpecEst
An Analysis Toolbox for Hermitian Positive Definite Matrices
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 (non-degenerate) covariance matrices or spectral density matrices.
The tools in this package can be used to perform:
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Intrinsic manifold wavelet regression and clustering for curves (1D) or surfaces (2D) of Hermitian positive definite matrices. These implementations are based in part on the paper (Chau and von Sachs 2017).
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Exploratory data analysis and inference for samples of Hermitian positive definite matrices by means of intrinsic manifold data depth and manifold rank-based hypothesis tests. These implementations are based on the paper (Chau, Ombao, and von Sachs 2017).
For more details and examples on how to use the package see the accompanying vignettes in the vignettes folder.
A demo Shiny app to test out the implemented functions in the package is available here.
Author and maintainer: Joris Chau ([email protected]).
Installation
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Stable CRAN version: install from within R
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Current development version: install via
devtools::install_github("JorisChau/pdSpecEst")
References
Chau, J., and R. von Sachs. 2017. “Positive Definite Multivariate Spectral Estimation: A Geometric Wavelet Approach.” http://arxiv.org/abs/1701.03314.
Chau, J., H. Ombao, and R. von Sachs. 2017. “Data Depth and Rank-Based Tests for Covariance and Spectral Density Matrices.” http://arxiv.org/abs/1706.08289.
News
pdSpecEst 1.2.1
- Removed unnecessary package imports
pdSpecEst 1.2.0
- New and updated features:
- Updated 1D intrinsic wavelet regression and clustering with
pdSpecEst1DandpdSpecClust1Dbased on various new metrics - 2D intrinsic wavelet regression and clustering with
pdSpecEst2DandpdSpecClust2D - New tools for intrinsic 1D and 2D polynomial generation and interpolation
- Time-varying periodograms with
pdPgram2D - Tree-structured 1D and 2D wavelet thresholding with
pdCART - Depth-based intrinsic confidence regions with
pdConfInt1D - New example spectral matrices and benchmark procedures
- Updated 1D intrinsic wavelet regression and clustering with
- New and updated functions:
H.coeff,InvWavTransf1D,InvWavTransf2D,ParTrans,pdCART,pdConfInt1D,pdDepth,pdMean,pdNeville,pdPgram2D,pdPolynomial,pdRankTests,pdSpecClust1D,pdSpecClust2D,pdSpecEst1D,pdSpecEst2D,pdSplineReg,rExamples,rExamples2D,WavTransf1D,WavTransf2D - Updated vignettes: "Wavelet-based multivariate spectral analysis"
- Updated Shiny app (see README or DESCRIPTION for url)
pdSpEcEst 1.1.1
- New features: data depth and rank-based hypothesis tests for samples of Hermitian PD matrices
- New functions:
pdDist,pdDepth,pdRankTests - New vignette: "Data depth and rank-based tests for HPD matrices"
- New demo Shiny app (see README or DESCRIPTION for url)
pdSpecEst 1.0.0
- New release