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Local polynomial regression for symmetric positive definite matrices

Author

Listed:
  • Ying Yuan
  • Hongtu Zhu
  • Weili Lin
  • J. S. Marron

Abstract

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Suggested Citation

  • Ying Yuan & Hongtu Zhu & Weili Lin & J. S. Marron, 2012. "Local polynomial regression for symmetric positive definite matrices," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(4), pages 697-719, September.
    • Handle: RePEc:bla:jorssb:v:74:y:2012:i:4:p:697-719
    DOI: j.1467-9868.2011.01022.x
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    Citations

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    Cited by:

    1. Gouriéroux, Christian & Monfort, Alain & Zakoian, Jean-Michel, 2017. "Pseudo-Maximum Likelihood and Lie Groups of Linear Transformations," MPRA Paper 79623, University Library of Munich, Germany.
    2. Bailly, Gabriel & von Sachs, Rainer, 2024. "Time-Varying Covariance Matrices Estimation by Nonlinear Wavelet Thresholding in a Log-Euclidean Riemannian Manifold," LIDAM Discussion Papers ISBA 2024004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. C. Gouriéroux & A. Monfort & J.‐M. Zakoïan, 2019. "Consistent Pseudo‐Maximum Likelihood Estimators and Groups of Transformations," Econometrica, Econometric Society, vol. 87(1), pages 327-345, January.
    4. Lizhen Lin & Brian St. Thomas & Hongtu Zhu & David B. Dunson, 2017. "Extrinsic Local Regression on Manifold-Valued Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1261-1273, July.
    5. Chau, Van Vinh & von Sachs, Rainer, 2018. "Intrinsic wavelet regression for surfaces of Hermitian positive definite matrices," LIDAM Discussion Papers ISBA 2018025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Rabi Bhattacharya & Rachel Oliver, 2019. "Nonparametric Analysis of Non-Euclidean Data on Shapes and Images," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-36, February.
    7. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Emil Cornea & Hongtu Zhu & Peter Kim & Joseph G. Ibrahim, 2017. "Regression models on Riemannian symmetric spaces," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 463-482, March.
    9. Xiongtao Dai & Zhenhua Lin & Hans‐Georg Müller, 2021. "Modeling sparse longitudinal data on Riemannian manifolds," Biometrics, The International Biometric Society, vol. 77(4), pages 1328-1341, December.
    10. Krebs, Johannes & Rademacher, Daniel & von Sachs, Rainer, 2022. "Statistical inference for intrinsic wavelet estimators of SPD covariance matrices in a log-Euclidean manifold," LIDAM Discussion Papers ISBA 2022004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Zhou Lan & Brian J. Reich & Joseph Guinness & Dipankar Bandyopadhyay & Liangsuo Ma & F. Gerard Moeller, 2022. "Geostatistical modeling of positive‐definite matrices: An application to diffusion tensor imaging," Biometrics, The International Biometric Society, vol. 78(2), pages 548-559, June.
    12. Ian L. Dryden & Kwang-Rae Kim & Huiling Le, 2019. "Bayesian Linear Size-and-Shape Regression with Applications to Face Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 83-103, February.
    13. Chau, Joris & von Sachs, Rainer, 2022. "Time-varying spectral matrix estimation via intrinsic wavelet regression for surfaces of Hermitian positive definite matrices," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    14. Ki, Dohyeong & Park, Byeong U., 2021. "Intrinsic Hölder classes of density functions on Riemannian manifolds and lower bounds to convergence rates," Statistics & Probability Letters, Elsevier, vol. 169(C).
    15. Pigoli, Davide & Menafoglio, Alessandra & Secchi, Piercesare, 2016. "Kriging prediction for manifold-valued random fields," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 117-131.

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