18.465 | Spring 2005 | Graduate

Topics in Statistics: Nonparametrics and Robustness

Course Description

This graduate-level course focuses on one-dimensional nonparametric statistics developed mainly from around 1945 and deals with order statistics and ranks, allowing very general distributions.

For multidimensional nonparametric statistics, an early approach was to choose a fixed coordinate system and work with order …

This graduate-level course focuses on one-dimensional nonparametric statistics developed mainly from around 1945 and deals with order statistics and ranks, allowing very general distributions.

For multidimensional nonparametric statistics, an early approach was to choose a fixed coordinate system and work with order statistics and ranks in each coordinate. A more modern method, to be followed in this course, is to look for rotationally or affine invariant procedures. These can be based on empirical processes as in computer learning theory.

Robustness, which developed mainly from around 1964, provides methods that are resistant to errors or outliers in the data, which can be arbitrarily large. Nonparametric methods tend to be robust.

Course Info

Learning Resource Types
Lecture Notes
Problem Sets
Graph of two sample data with an outlier.
Two-sample data with an outlier from Problem set 1, problems 4-5. (Image courtesy of OCW.)