References
- Antoniadis, A. (1997), “Wavelets in Statistics: A Review,” Statistical Methods & Applications, 6, 97–130. DOI: https://doi.org/10.1007/BF03178905.
- Bhatia, R. (2009), Positive Definite Matrices, Princeton, NJ: Princeton University Press.
- Boumal, N., and Absil, P.-A. (2011a), “A Discrete Regression Method on Manifolds and Its Application to Data on SO(n),” IFAC Proceedings Volumes, 44, 2284–2289. DOI: https://doi.org/10.3182/20110828-6-IT-1002.00542.
- Boumal, N., and Absil, P.-A. (2011b), “Discrete Regression Methods on the Cone of Positive-Definite Matrices,” in IEEE ICASSP 2011, pp. 4232–4235.
- Brillinger, D. (1981), Time Series: Data Analysis and Theory, San Francisco, CA: Holden-Day.
- Brockwell, P., and Davis, R. (2006), Time Series: Theory and Methods, New York: Springer.
- Chau, J. (2017), “pdSpecEst: An Analysis Toolbox for Hermitian Positive Definite Matrices,” R Package Version 1.2.3, available at https://CRAN.R-project.org/package=pdSpecEst.
- Chau, J. (2018), “Advances in Spectral Analysis for Multivariate, Nonstationary and Replicated Time Series,” Ph.D. thesis, Université Catholique de Louvain.
- Chau, J., Ombao, H., and R. von Sachs (2019), “Intrinsic Data Depth for Hermitian Positive Definite Matrices,” Journal of Computational and Graphical Statistics, 28, 427–439. DOI: https://doi.org/10.1080/10618600.2018.1537926.
- Dahlhaus, R. (2012), “Locally Stationary Processes,” in Time Series Analysis: Methods and Applications (Vol. 30), eds. Rao T. S. and Rao S. S. and Rao C. R. Amsterdam: Elsevier, pp. 351–413.
- Dai, M., and Guo, W. (2004), “Multivariate Spectral Analysis Using Cholesky Decomposition,” Biometrika, 91, 629–643. DOI: https://doi.org/10.1093/biomet/91.3.629.
- do Carmo, M. (1992), Riemannian Geometry, Boston, MA: Birkhäuser.
- Donoho, D. (1993), “Smooth Wavelet Decompositions With Blocky Coefficient Kernels,” in eds. Schumaker L. L. and Webb G. Recent Advances in Wavelet Analysis, New York: Academic Press, pp. 259–308.
- Donoho, D. (1997), “Cart and Best-Ortho-Basis: A Connection,” The Annals of Statistics, 25, 1870–1911.
- Dryden, I., Koloydenko, A., and Zhou, D. (2009), “Non-Euclidean Statistics for Covariance Matrices, With Applications to Diffusion Tensor Imaging,” The Annals of Applied Statistics, 3, 1102–1123. DOI: https://doi.org/10.1214/09-AOAS249.
- Fiecas, M., and Ombao, H. (2016), “Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment,” Journal of the American Statistical Association, 111, 1440–1453. DOI: https://doi.org/10.1080/01621459.2016.1165683.
- Gorrostieta, C., Ombao, H., Prado, R., Patel, S., and Eskandar, E. (2012), “Exploring Dependence Between Brain Signals in a Monkey During Learning,” Journal of Time Series Analysis, 33, 771–778. DOI: https://doi.org/10.1111/j.1467-9892.2011.00767.x.
- Hinkle, J., Fletcher, P., and Joshi, S. (2014), “Intrinsic Polynomials for Regression on Riemannian Manifolds,” Journal of Mathematical Imaging and Vision, 50, 32–52. DOI: https://doi.org/10.1007/s10851-013-0489-5.
- Holbrook, A., Lan, S., Vandenberg-Rodes, A., and Shahbaba, B. (2018), “Geodesic Lagrangian Monte Carlo Over the Space of Positive Definite Matrices: With Application to Bayesian Spectral Density Estimation,” Journal of Statistical Computation and Simulation, 88, 982–1002. DOI: https://doi.org/10.1080/00949655.2017.1416470.
- Jansen, M., and Oonincx, P. (2005), Second Generation Wavelets and Applications, London: Springer-Verlag.
- Klees, R., and Haagmans, R. (2000), Wavelets in the Geosciences, Berlin: Springer-Verlag.
- Krafty, R., and Collinge, W. (2013), “Penalized Multivariate Whittle Likelihood for Power Spectrum Estimation,” Biometrika, 100, 447–458. DOI: https://doi.org/10.1093/biomet/ass088.
- Lang, S. (1995), Differential and Riemannian Manifolds, New York: Springer-Verlag.
- Ma, Y., and Fu, Y. (2012), Manifold Learning Theory and Applications, London: CRC Press, Taylor & Francis.
- Pasternak, O., Sochen, N., and Basser, P. (2010), “The Effect of Metric Selection on the Analysis of Diffusion Tensor MRI Data,” NeuroImage, 49, 2190–2204. DOI: https://doi.org/10.1016/j.neuroimage.2009.10.071.
- Pennec, X. (2006), “Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements,” Journal of Mathematical Imaging and Vision, 25, 127–154. DOI: https://doi.org/10.1007/s10851-006-6228-4.
- Pennec, X., Fillard, P., and Ayache, N. (2006), “A Riemannian Framework for Tensor Computing,” International Journal of Computer Vision, 66, 41–66. DOI: https://doi.org/10.1007/s11263-005-3222-z.
- Rahman, I., Drori, I., Stodden, V., Donoho, D., and Schröder, P. (2005), “Multiscale Representations for Manifold-Valued Data,” Multiscale Modeling & Simulation, 4, 1201–1232. DOI: https://doi.org/10.1137/050622729.
- Rosen, O., and Stoffer, D. (2007), “Automatic Estimation of Multivariate Spectra via Smoothing Splines,” Biometrika, 94, 335–345. DOI: https://doi.org/10.1093/biomet/asm022.
- Said, S., Bombrun, L., Berthoumieu, Y., and Manton, J. (2017), “Riemannian Gaussian Distributions on the Space of Symmetric Positive Definite Matrices,” IEEE Transactions on Information Theory, 63, 2153–2170. DOI: https://doi.org/10.1109/TIT.2017.2653803.
- Smith, S. (2000), “Intrinsic Cramér-Rao Bounds and Subspace Estimation Accuracy,” in Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop, IEEE, pp. 489–493.
- Villani, C. (2009), Optimal Transport: Old and New, Berlin: Springer-Verlag.
- Wahba, G. (1980), “Automatic Smoothing of the Log Periodogram,” Journal of the American Statistical Association, 75, 122–132. DOI: https://doi.org/10.1080/01621459.1980.10477441.
- Walden, A. (2000), “A Unified View of Multitaper Multivariate Spectral Estimation,” Biometrika, 87, 767–788. DOI: https://doi.org/10.1093/biomet/87.4.767.
- Walnut, D. (2002), An Introduction to Wavelet Analysis, Boston, MA: Birkhäuser.
- Yuan, Y., Zhu, H., Lin, W., and Marron, J. (2012), “Local Polynomial Regression for Symmetric Positive Definite Matrices,” Journal of the Royal Statistical Society, Series B, 74, 697–719. DOI: https://doi.org/10.1111/j.1467-9868.2011.01022.x.
- Zheng, H., Tsui, K.-W., Kang, X., and Deng, X. (2017), “Cholesky-Based Model Averaging for Covariance Matrix Estimation,” Statistical Theory and Related Fields, 1, 48–58. DOI: https://doi.org/10.1080/24754269.2017.1336831.
- Zhu, H., Chen, Y., Ibrahim, J., Li, Y., Hall, C., and Lin, W. (2009), “Intrinsic Regression Models for Positive-Definite Matrices With Applications to Diffusion Tensor Imaging,” Journal of the American Statistical Association, 104, 1203–1212. DOI: https://doi.org/10.1198/jasa.2009.tm08096.