Topics in Statistics: Nonparametrics and Robustness
A graduate MIT OpenCourseWare course covering the two branches of statistics that don't lean on assumed distributions. The first half traces one-dimensional nonparametric methods built from around 1945 onward, working with order statistics and ranks so that inference holds under very general distributions rather than assuming normality. The course then moves into multidimensional nonparametrics, contrasting the older fixed-coordinate approach to order statistics with the more modern rotationally and affine invariant procedures, some built on empirical processes borrowed from computer learning theory. The second half covers robustness, developed mainly after 1964, which studies estimators that stay stable when data contains outliers or errors of arbitrary size, and shows why nonparametric methods tend to be robust by construction. Materials include MIT's lecture notes and readings for self-study, free to access under MIT OpenCourseWare's standard license, with no certificate offered. This is dense, proof-oriented material aimed at students who already have a solid grounding in mathematical statistics.