Statistics 240: Nonparametric and Robust Methods. Fall 2010
This year, the course will emphasize permutation tests. "Permutation" is meant abstractly: it is the action of any group operation, not simply the permutation group on n objects. We will be concerned with identifying invariances that the probability distribution of the data should satisfy if the null hypothesis is true, then evaluating whether the data give evidence against the invariance. There will be examples from psychology, genetics, seismology, astrophysics, political science, accounting, …
- Randomization models and "natural" group invariances under the null hypothesis.
- Randomized experiments, natural experiments, and hypothetical randomization
- The Neyman model and its generalizations
- Tests and confidence intervals based on ranks
- Abstract permutation tests: nonparametric hypotheses including exhangeability, symmetry, independence; choosing the test statistic
- Simulation and random number generation.
- Analytic and numerical approximations of nonparametric tests.
- Nonparametric inference in financial and electoral auditing.
- Bootstrap estimates, tests and confidence intervals; the jackknife.
- Robust estimates of location and scale, M estimates (time permitting)
- Kernel and nearest-neighbor density estimates; cross validation (time permitting)
- One year of upper-division probability and statistics; programming in R, MATLAB, or a similar high-level language.
Recommended Texts (no required text)
- Lehmann, E.L. (1998). Nonparametrics: Statistical Methods Based on Ranks, Prentice Hall, Upper Saddle River, NJ.
- Freedman, D.A. (2005). Statistical Models: Theory and Practice, Cambridge University Press.
Grading. Grades will be based on assignments, a term project, and a final exam.