References
- Atkinson, A. C, and M. Riani. 2000. Robust diagnostic regression analysis. New York: Springer.
- Butler, R. W., P. L. Davies, and M. Jhun. 1993. Asymptotics for the minimum covariance determinant estimator. Annals of Statistics 21:1385–400.
- Cator, E. A, and H. P. Lopuhaä. 2012. Central limit theorem and influence function for the MCD estimators at general multivariate distributions. Bernoulli 18 (2):520–51. doi:10.3150/11-BEJ353.
- Cerioli, A. 2010. Multivariate outlier detectionwith high-breakdown estimators. Journal of the American Statistical Association 105 (489):147–56. doi:10.1198/jasa.2009.tm09147.
- Cerioli, A., A. Farcomeni, and M. Riani. 2019. Wild adaptive trimming for robust estimation and cluster analysis. Scandinavian Journal of Statistics 46 (1):235–56. doi:10.1111/sjos.12349.
- Corder, G. W, and D. I. Foreman. 2014. Nonparametric statistics: A step-by-step approach. 2nd ed. New York: Wiley.
- Davies, P. L. 1992. The asymptotics of Rousseeuw’s minimum volume ellipsoid estimator. Annals of Statistics 20:1828–43.
- Dick, J., F. Y. Kuo, and I. H. Sloan. 2013. High-dimensional integration: The quasi-Monte Carlo way. Acta Numerica 22:133–288. doi:10.1017/S0962492913000044.
- Donoho, D. L, and P. J. Huber. 1983. The notion of breakdown point, In A Festschrift for Erich L. Lehmann, eds. P.J. Bickel, K.A. Doksum and J.L. Hodges, 157–84. Belmont, CA: Wadsworth.
- Donoho, D. L, and R. C. Liu. 1994. The “automatic” robustness of minimum distance functional. Annals of Statistics 16:552–86.
- Ekiz, M, and O. U. Ekiz. 2017. Outlier detection with Mahalanobis square distance: Incorporating small sample correction factor. Journal of Applied Statistics 44 (13):2444–57. doi:10.1080/02664763.2016.1255313.
- Fan, J., F. Han, and H. Liu. 2014. Challenges of Big Data analysis. National Science Review 1 (2):293–314. doi:10.1093/nsr/nwt032.
- Gervini, D, and V. J. Yohai. 2002. A class of robust and fully efficient regression estimators. Annals of Statistics 30:583–616.
- Huber, P. J. 1981. Robust statistics. New York: Wiley.
- Hubert, M., M. Debruyne, and P. J. Rousseeuw. 2018. Minimum covariance determinant and extensions. WIREs Computational Statistics 10 (3):e1421. doi:10.1002/wics.1421.
- Hubert, M., P. J. Rousseeuw, and S. Van Aelst. 2008. High-breakdown robust multivariate methods. Statistical Science 23 (1):92–119. doi:10.1214/088342307000000087.
- Mu, W, and S. Xiong. 2017. Robust generalized confidence intervals. Communications in Statistics – Simulation and Computation 46 (8):6049–60. doi:10.1080/03610918.2016.1189566.
- Riani, M., A. C. Atkinson, and A. Cerioli. 2009. Finding an unknown number of multivariate outliers. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 71 (2):447–66. doi:10.1111/j.1467-9868.2008.00692.x.
- Riani, M., D. Perrotta, and A. Cerioli. 2015. The forward search for very large datasets. Journal of Statistical Software 67 (1):1–20. doi:10.18637/jss.v067.c01.
- Rousseeuw, P. J. 1985. Multivariate estimation with high breakdown point. In Mathematical statistics and applications, B, eds. W. Grossmann, G. Pflug, I. Vincze and W. Wertz. Dordrecht: Reidel Publishing Company.
- Rousseeuw, P. J, and K. Van Driessen. 1999. A fast algorithm for the minimum covariance determinant estimator. Technometrics 41 (3):212–23. doi:10.1080/00401706.1999.10485670.
- Wolfowitz, J. 1957. The minimum distance method. The Annals of Mathematical Statistics 28 (1):75–88. doi:10.1214/aoms/1177707038.
- Wu, J., R. Karunamuni, and B. Zhang. 2012. Efficient Hellinger distance estimates for semiparametric models. Journal of Multivariate Analysis 107:1–23. doi:10.1016/j.jmva.2012.01.007.
- Xiong, S. 2020. On Huber’s contaminated models. Technical Report, Chinese Academy of Sciences.
- Xiong, S, and V. R. Joseph. 2013. Regression with outlier shrinkage. Journal of Statistical Planning and Inference 143 (11):1988–2001. doi:10.1016/j.jspi.2013.06.007.