Part I: An introduction to robust statistics.
Lecturers: Prof. Anthony Atkinson, London School of Economics, UK, and
Prof. Marco Riani, University of Parma, Italy.
Sessions 1, 2 and 3 of Module I.
Duration: 6 hours.
Abstract: Data corrupted by outliers are ubiquitous. Robust statistical methods are designed to provide fitted models which are unaffected by outliers. They also, ideally, should provide information about departures from the assumed model.
Each topic in the course will be introduced both algebraically and through examples. The topics will be illustrated in a variety of data settings using the highly interactive MATLAB toolbox FSDA, which is freely downloadable.
The robust methods to be described include downweighting methods, such as M and S estimation in which extreme observations are given reduced weight; hard trimming methods in which the best fit is obtained for a prespecified proportion of the data and flexible trimming using the forward search. We compare and contrast the properties of these methods in a variety of settings.
The course begins with multiple regression. We then consider robust transformations of the response. A second part is robust methods for multivariate data. We start with a single sample and then consider robust clustering.
The computer sessions will illustrate, in several of these settings, the use of linking and brushing plots to gain an understanding of how observations, individually or in clusters, are affecting conclusions drawn form the data.
An introductory text, now somewhat dated, is "Robust Diagnostic Regression Analysis" by A.C. Atkinson and M. Riani (Springer, 2000). The toolbox contains descriptions and examples of all techniques to be discussed.
Material: Regression Slides Multivariate Slides

Part II: Robust Methods for Econometrics
Title: Validity-Robust Semiparametrically Efficient Inference for Nonlinear Time Series Models
Lecturer: Prof. Marc Hallin, Universite Libre de Bruxelles, Belgium.
Sessions 4 and 5 of Module I.
Duration: 4 hours
Abstract: Nonlinear time series models play an important role in a number of econometric problems; they are pervasive in financial econometrics. Examples include AR-ARCH models, discretely observed non-Gaussian Ornstein-Uhlenbeck processes, autoregressive conditional duration models for irregularlysampled data, ... Although Gaussian assumptions, in that context, are quite unrealistic, Gaussian quasi-likelihood procedures (for estimation and testing) remain the most popular approach. Those methods, typically, are not validity-robust---namely, their validity (asymptotic probability level for tests, root-n consistency for estimators) is not guaranteed.
In principle, traditional semiparametric inference methods (in the style of Bickel et al. 1993) offer a theoretical alternative. However, they require tedious tangent space calculations, and the estimation of the actual innovation density. The objective of this tutorial is to show that rank-based inference constitutes a convenient substitute for those methods, and yield validity-robust tests and estimators reaching semiparametric efficiency bounds without running into the difficulties of tangent space calculation and density estimation.
Material: Paper1 Paper2 Paper3
Slides: Tutorial LeCam in a Nutshell Semiparametrics Regression Stable