Stochastic Systems Group  

Standard statistics, such as the sample mean and covariance, are sometimes applied without serious thought to their appropriateness. In the case of the sample mean and covariance, this is largely due to their squarederror optimality under \iid conditions; however, these estimates are not robust to deviations from the model. In fact, the estimates can be made arbitrarily poor, by the corruption of a single data point. It is the goal of robust estimation to develop methods that are not only robust to outliers, but also perform well under the correct model.
In this talk, we will survey robust estimation techniques specifically tailored to estimating multivariate location and scatter. Particular attention will be paid to three methods: Mestimators, Sestimators, and the Minimum Covariance Determinant (MCD) estimator. The intuition behind these estimators is to find the location and covariance estimate by trying to simultaneously identify and downweight outliers in your estimates; although, they do so in different ways.
This talk is a based on my Area Exam. The associated report along
with the papers surveyed can be obtained from web site:
http://ssg.mit.edu/~ajkim/area_exam
Problems with this site should be emailed to jonesb@mit.edu