Předmět Robust statistics and econometrics (JEM160)

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Materiál	Typ	Datum	Počet stažení

Cíl

To enlarge the theoretical knowledge of regression analysis over its classical framework  of (statistical or econometric) explanation. Moreover, to allow the students to look over the horizon of usual mathematically exactly constructed approach of formalized modelling, i.e. to offer an insight into such aspects ofmathematical, formalized description of universe which we can meet  neither in the statistical nor the econometric texts. The content of the course can be decently accommodated to the topics of study and of interest of the attendants.

Sylabus

Robust statistics and ekonometrics as a complement to the classical methods. Inspirations for robust approach - differences with respect to the classical approach.Main problems and main goals of robust statistics and econometrics. 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.Classical and newly proposed characteristics of point estimators the gross-error and the local-shift sensitivity, the rejection  and the breakdown point .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.The most frequent families of robust estimators - M, L, R, the minimal distance and the minimal volume estimators, etc.Historical survey: from  to over the regression quantiles to Looking for the algorithm, its implementation and verification - patterns of processing the data, sequential estimation of contamination level by means of LTS, forward search.From the minimization of median of the squared residuals and of the least trimmed squares to the least weighted squares.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.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.Robustification of alternative methods (alternative to the ordinary least squares or the maximum likelihood)  as the instrumental variables, orthogonal or ridge regression.Robustification of classical characteristics of quality of model - significance of the individual explanatory variable, tests of submodels, robustification of  the classical diagnostic tools - Durbin-Watson, White , Hausman or Chow test for robust estimation.Examples of robust processing the panel data - the model with fixed and random effects, gravitational model.Philosophy of the formalized modeling with short excursions into the history of processing the data.

Literatura

Literature:Atkinson, A.C., M. Riani (2002) :  Exploring Multivariate Data with the Forward Search.  Springer.Chatterjee, S., Hadi, A. S. (1988): Sensitivity Analysis in Linear Regression. New York: J. Wiley and Sons. Dutter,R.,  P. Filzmoser, P. J. Rousseeuw (2003) :  Development in Robust Statistics.  Springer.Hampel, F. R., E. M. Ronchetti, P.  J. Rousseeuw, W.  A. Stahel (1986):  Robust  Statistics -- The Approach Based on Influence Functions.  New York 1986,  J.Wiley  and Son.Huber, P.J.(1981):  Robust Statistics. New York: J.Wiley and Sons.Judge, G. G., Griffiths, W. E., Hill, R. C., Lutkepohl, H., Lee, T. C. (1985):  The Theory and Practice of Econometrics. New York 1985,  J.Wiley and Sons (second edition).Rousseeuw, P. J., A. M. Leroy (1987): Robust Regression and Outlier Detection.  New York 1987, J.Wiley and Sons. Štěpán, J. (1987):  Teorie pravděpodobnosti.  Praha 1987 Academia. Víšek, J. Á. : Papers according to the interest of participants , see  http://ies.fsv.cuni.cz/sci/publication/user/id/58/lang/en .Zvára, K. (1989): Regresní analýza. Praha 1989, Academia.   

Garant

prof. RNDr. Jan Ámos Víšek, CSc.