Here’s a video I put together as part of a job application process discussing the concept of robustness and highlighting the aim of robust estimators.
The slides are here: https://garthtarr.com/pres/RobIntro
Note that you may need to refresh the slides to get the network graphs to appear.
References:
Location: Hodges-Lehmann estimator
http://en.wikipedia.org/wiki/Hodges-Lehmann_estimator
Hodges, Lehmann (1963). Estimation of location based on ranks. Annals of Mathematical Statistics 34(2): 598-611. DOI: 10.1214/aoms/1177704172
Covariance: Minimum Covariance Determinant (MCD) estimator
Hubert, Debruyne (2010). Minimum covariance determinant. Wiley Interdisciplinary Reviews: Computational Statistics, 2: 36-43. DOI: 10.1002/wics.61
Sparse precision matrix estimation: Graphical lasso
Friedman, Hastie, Tibshirani (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3): 432-441. DOI: 10.1093/biostatistics/kxm045
Robust precision matrix estimation
Tarr, Müller, Weber (2015). Robust estimation of precision matrices under cellwise contamination. Computational Statistics & Data Analysis, to appear. DOI: 10.1016/j.csda.2015.02.005
Robust scale estimation
Tarr, Müller, Weber (2012). A robust scale estimator based on pairwise means. Journal of Nonparametric Statistics, 24(1): 187-199. DOI: 10.1080/10485252.2011.621424
Overview of robust estimation of scale and dependence
Tarr, (2014). Quantile Based Estimation of Scale and Dependence. PhD Thesis. University of Sydney, Australia. hdl.handle.net/2123/10590