Intrinsic Wavelet Regression for Curves of Hermitian Positive Definite Matrices
| Autor: | Rainer von Sachs, Joris Chau |
|---|---|
| Přispěvatelé: | UCL - SSH/IMMAQ/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles, UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Pure mathematics Hermitian positive definite matrices ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION MathematicsofComputing_NUMERICALANALYSIS Data_CODINGANDINFORMATIONTHEORY Positive-definite matrix Space (mathematics) 01 natural sciences Multivariate nonstationary time series Methodology (stat.ME) 62M15 62G08 010104 statistics & probability symbols.namesake Wavelet Fourier spectral matrix Time-varying spectral matrix estimation Wavelet regression 0502 economics and business Surface wavelet transform Affine-invariant metric 0101 mathematics Multivariate time series Statistics - Methodology 050205 econometrics Mathematics Wavelet thresholding Riemannian manifold 05 social sciences Wavelet transform Intrinsic wavelet transform Hermitian matrix Fourier transform symbols Statistics Probability and Uncertainty |
| Zdroj: | Journal of the American Statistical Association, Vol. 116, no. 534, p. 819-832 (2021) |
| DOI: | 10.6084/m9.figshare.11339471.v2 |
| Popis: | Intrinsic wavelet transforms and wavelet estimation methods are introduced for curves in the non-Euclidean space of Hermitian positive definite matrices, with in mind the application to Fourier spectral estimation of multivariate stationary time series. The main focus is on intrinsic average-interpolation wavelet transforms in the space of positive definite matrices equipped with an affine-invariant Riemannian metric, and convergence rates of linear wavelet thresholding are derived for intrinsically smooth curves of Hermitian positive definite matrices. In the context of multivariate Fourier spectral estimation, intrinsic wavelet thresholding is equivariant under a change of basis of the time series, and nonlinear wavelet thresholding is able to capture localized features in the spectral density matrix across frequency, always guaranteeing positive definite estimates. The finite-sample performance of intrinsic wavelet thresholding is assessed by means of simulated data and compared to several benchmark estimators in the Riemannian manifold. Further illustrations are provided by examining the multivariate spectra of trial-replicated brain signal time series recorded during a learning experiment. Supplementary materials for this article are available online. |
| Databáze: | OpenAIRE |
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