Tutorial: Introduction to Robust Statistics with R

Martin Mächler, ETH Zurich, Zurich, Switzerland.
Elvezio Ronchetti, University of Geneva, Geneva, Switzerland.

Abstract

Classical statistics relies on parametric models. Typically, assumptions are made on the structural and the stochastic parts of the model and optimal procedures are derived under these assumptions. Standard examples are least squares estimators in linear models and their extensions, maximum likelihood estimators, and the corresponding likelihood-based tests.

Robust statistics deals with deviations from the stochastic assumptions and their dangers for classical estimators and tests and develops statistical procedures which are still reliable and reasonably efficient in the presence of such deviations. It can be viewed as a statistical theory dealing with approximate parametric models by providing a reasonable compromise between the rigidity of a strict parametric approach and the potential difficulties of interpretation of a fully nonparametric analysis.

This tutorial will give a brief introduction to robust statistics by reviewing some basic general concepts and tools and by showing how they can be used in data analysis, especially in the framework of linear and generalized linear models, to provide an alternative complementary statistical analysis with additional useful information.

We will use R functions mainly from packages 'MASS' and CRAN packages 'robustbase' and 'robust'. There will be handouts and R scripts available to the course participants.

Topics

Introduction (general idea, extension of classical statistics)
Basic concepts and tools (sensitivity curve, influence function, breakdown point)
Robust estimation, inference, and variable selection
Linear models
Generalized linear models
Elements of multivariate analysis, notably robust estimation of location and covariance.

Literature

(in addition to handouts)

Maronna, R.A., Martin, R.D., and Yohai, V.J. (2006). Robust Statistics, Theory and Methods, Wiley, New York.
Huber P.J. (1981). Robust Statistics, Wiley, New York (paperback 2004).
Hampel F. R., Ronchetti E. M., Rousseeuw P.J., and Stahel W.A. (1986). Robust Statistics: The Approach Based on Influence Functions, Wiley, New York (paperback 2005).