Syllabus
1) Robust statistics and ekonometrics as a complement to the classical methods. Inspirations for robust approach - differences with respect to the classical approach.
2) Proposals by Peter Huber versus an approach by Frank Hampel - the global versus the local approach, Prokhorov versus Kolmogorov-Smirnov metric, examples of convergence of sequences of d.f.‘s.
3) Classical and newly proposed characteristics of point estimators - significance of the individual explanatory variable (in the classical as well as in the robust version), tsts of submodels (again, classically and robustly), the gross-error and the local-shift sensitivity, the rejection and the breakdown point .
4) Specifications of these characteristics for the basic statistical and econometric tasks - the location and the scale parameter, the regression model. Role of invariance and equivariance in the (robust) point estimation.
5) The most frequent families of robust estimators - M, L, R, the minimal distance and the minimal volume estimators, etc.
6) Historical survey: from to over the regression quantiles to the minimization of median of the squared residuals and to the least trimmed squares.
7) Looking for the algorithm, its implementation and verification - patterns of processing the data, sequential estimation of contamination level by means of LTS, forward search.
8) Proving methods - Skorohod imbedding into the Wiener process, generalization of Kolmogorov-Smirnov results about the uniform convergence of empirical d.f.’s to the theoretical (“underlying”) d.f. in the regression framework.
9) Problems with the high breakdown point - the large sensitivity to the deletion/inclusion of one observation and to a shift of inliers. Solution of this problem by the least weighted squares.
10) Robustification of alternative methods (alternative to the ordinary least squares or the maximum likelihood) as the instrumental variables, orthogonal or ridge regression.
11) Robustification of the classical diagnostic tools - Durbin-Watson, White , Hausman or Chow test for robust estimation.
12) Examples of robust processing the panel data - the model with fixed and random effects, gravitational model.
13) Philosophy of the formalized modeling with short excursions into the history of processing the data.
Annotation
Non-traditional view on the regression analysis as a tool for model bulding as well as a tool of structure analysis of data, alternative methods (to OLS and ML) of estimation and for them modified classical diagnostic tools for specification of model, historical roots and philosophical consequences.