References

The MVP documentation cites the following robust-statistics and covariance-estimation background. The implementation is intentionally pragmatic and experimental; these references provide the mathematical context rather than a claim that every estimator is a line-by-line reproduction of a specific paper.

Robust covariance and MCD

      1. Rousseeuw. 1984. Least median of squares regression. Journal of the American Statistical Association.

      1. Rousseeuw. 1985. Multivariate estimation with high breakdown point. In Mathematical Statistics and Applications.

      1. Rousseeuw and K. Van Driessen. 1999. A fast algorithm for the minimum covariance determinant estimator. Technometrics.

    1. Hubert, M. Debruyne, and P. J. Rousseeuw. 2018. Minimum covariance determinant and extensions. WIREs Computational Statistics.

Tyler and robust scatter M-estimation

      1. Tyler. 1987. A distribution-free M-estimator of multivariate scatter. The Annals of Statistics.

      1. Maronna. 1976. Robust M-estimators of multivariate location and scatter. The Annals of Statistics.

    1. Ollila, D. E. Tyler, V. Koivunen, and H. V. Poor. 2012. Complex elliptically symmetric distributions: survey, new results and applications. IEEE Transactions on Signal Processing.

Regularization and shrinkage

    1. Ledoit and M. Wolf. 2004. A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis.

    1. Chen, A. Wiesel, and A. O. Hero. 2011. Robust shrinkage estimation of high-dimensional covariance matrices. IEEE Transactions on Signal Processing.

    1. Wiesel. 2012. Unified framework to regularized covariance estimation in scaled Gaussian models. IEEE Transactions on Signal Processing.

    1. Sun, P. Babu, and D. P. Palomar. 2014. Regularized Tyler’s scatter estimator: existence, uniqueness, and algorithms. IEEE Transactions on Signal Processing.

Matrix geometry and geodesic convexity

    1. Bhatia. 2007. Positive Definite Matrices. Princeton University Press.

    1. Sra and R. Hosseini. 2015. Conic geometric optimization on the manifold of positive definite matrices. SIAM Journal on Optimization.

    1. Moakher. 2005. A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM Journal on Matrix Analysis and Applications.

Heavy-tailed covariance and Student-t models

      1. Lange, R. J. A. Little, and J. M. G. Taylor. 1989. Robust statistical modeling using the t distribution. Journal of the American Statistical Association.

    1. McLachlan and T. Krishnan. 2008. The EM Algorithm and Extensions. Wiley.

      1. Maronna, R. D. Martin, V. J. Yohai, and M. Salibián-Barrera. 2019. Robust Statistics: Theory and Methods. Wiley.

Robust anomaly diagnostics

      1. Rousseeuw and A. M. Leroy. 1987. Robust Regression and Outlier Detection. Wiley.

    1. Hubert, P. J. Rousseeuw, and K. Vanden Branden. 2005. ROBPCA: a new approach to robust principal component analysis. Technometrics.

Robust clustering and mixtures

      1. Atkinson and M. Riani. 2000. Robust Diagnostic Regression Analysis. Springer.

    1. García-Escudero, A. Gordaliza, C. Matrán, and A. Mayo-Iscar. 2008. A general trimming approach to robust cluster analysis. The Annals of Statistics.

      1. McLachlan and D. Peel. 2000. Finite Mixture Models. Wiley.

      1. McLachlan and D. Peel. 1998/2000. Robust cluster analysis via mixtures of multivariate t-distributions. Related robust mixture-model literature.