18.465 | Spring 2005 | Graduate

# Topics in Statistics: Nonparametrics and Robustness

## Syllabus

### Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

### Prerequisite

A semester course in statistics such as Statistics for Applications (18.650) or Statistical Inference (the former 18.441)

### Overview

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.

### Textbook

A text for roughly half the course will be:

Randles, R. H., and D. A. Wolfe. Introduction to the Theory of Nonparametric Statistics. Malabar, FL: Krieger, 1991. ISBN: 0894645439.
(This book is currently out of print, but used copies may be available.)

For one or two lectures, we will use Section 2 of Chapter V, “Uniform and exponential spacings,” of the following book:

Devroye, L. Non-Uniform Random Variate Generation.  New York, NY: Springer-Verlag, 1986. ISBN: 3540406522.
(This book is also out of print, but the author made it available on the web.)

Near the end of the course, several lectures are based on the first twenty pages of the tutorial found in the following article:

Burges, C.J.C.  “A tutorial on support vector machines for pattern recognition.” Data Mining and Knowledge Discovery 2. Boston, MA: Kluwer Academic Publishers, 1998. pp. 121-167.

The above article also provides the material that problem set 8 is based on.

There will be supplementary handouts on several topics in the course, specifically on robustness and on multidimensional nonparametrics.

Grades will be determined by a weighted average of problem sets, the first exam, and the second exam. The second exam can be replaced by a term paper.

ACTIVITIES PERCENTAGES
Problem Sets 33.3%
First Exam 33.3%
Second Exam OR Term Paper 33.3%

### Assignments

There will be problem sets a little less than weekly. There will not be a final exam. The number (2 or 3) and scheduling of exams during the term will be decided by vote of students. Students who do well in the first two-thirds of the course will have the option of writing an expository paper on a topic relating to the course instead of taking the last exam.

Spring 2005
Lecture Notes
Problem Sets