fitHeavyTail-package | R Documentation |
Robust estimation methods for the mean vector, scatter matrix, and covariance matrix (if it exists) from data (possibly containing NAs) under multivariate heavy-tailed distributions such as angular Gaussian (via Tyler's method), Cauchy, and Student's t distributions. Additionally, a factor model structure can be specified for the covariance matrix. The latest revision also includes the multivariate skewed t distribution. The package is based on the papers: Sun, Babu, and Palomar (2014); Sun, Babu, and Palomar (2015); Liu and Rubin (1995); Zhou, Liu, Kumar, and Palomar (2019); Pascal, Ollila, and Palomar (2021).
fit_Tyler
, fit_Cauchy
, fit_mvt
, and fit_mvst
.
For a quick help see the README file: GitHub-README.
For more details see the vignette: CRAN-vignette.
Daniel P. Palomar and Rui Zhou
Ying Sun, Prabhu Babu, and Daniel P. Palomar, "Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithms," IEEE Trans. on Signal Processing, vol. 62, no. 19, pp. 5143-5156, Oct. 2014. <https://doi.org/10.1109/TSP.2014.2348944>
Ying Sun, Prabhu Babu, and Daniel P. Palomar, "Regularized Robust Estimation of Mean and Covariance Matrix Under Heavy-Tailed Distributions," IEEE Trans. on Signal Processing, vol. 63, no. 12, pp. 3096-3109, June 2015. <https://doi.org/10.1109/TSP.2015.2417513>
Chuanhai Liu and Donald B. Rubin, "ML estimation of the t-distribution using EM and its extensions, ECM and ECME," Statistica Sinica (5), pp. 19-39, 1995.
Chuanhai Liu, Donald B. Rubin, and Ying Nian Wu, "Parameter Expansion to Accelerate EM: The PX-EM Algorithm," Biometrika, Vol. 85, No. 4, pp. 755-770, Dec., 1998
Rui Zhou, Junyan Liu, Sandeep Kumar, and Daniel P. Palomar, "Robust factor analysis parameter estimation," Lecture Notes in Computer Science (LNCS), 2019. <https://arxiv.org/abs/1909.12530>
Esa Ollila, Daniel P. Palomar, and Frédéric Pascal, "Shrinking the Eigenvalues of M-estimators of Covariance Matrix," IEEE Trans. on Signal Processing, vol. 69, pp. 256-269, Jan. 2021. <https://doi.org/10.1109/TSP.2020.3043952>
Frédéric Pascal, Esa Ollila, and Daniel P. Palomar, "Improved estimation of the degree of freedom parameter of multivariate t-distribution," in Proc. European Signal Processing Conference (EUSIPCO), Dublin, Ireland, Aug. 23-27, 2021. <https://doi.org/10.23919/EUSIPCO54536.2021.9616162>
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