Regression Quantiles and Global Measures of Robustness

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Economists are constantly in search of more robust statistical techniques so that departures from standard assumptions will not disrupt the estimation process. Regression quantile methods and "breakdown" and "tail-behavior" measures, the foci of this research project, hold a great deal of promise for developing more robust alternatives. The specific objectives of the project with respect to regression quantiles are to refine the current methods and to develop user friendly algorithms and programs for applying these methods in linear models and related areas, further extending the theory to include dependent and non-stationary cases, to study dual regression quantiles and their corresponding rank statistics and to develop large dimension asymptotics where there are a large number of parameters. A second line of research involves global measures of robustness and their relation to outlier diagnostics. Analyses will be completed to understand more completely what causes statistical procedures to break down in the presence of outliers, particularly through the exploration of the close connection between finite-sample "breakdown" and "tail behavior" of estimators, and to refine current procedures for detecting and adjusting for outliers and to develop inference methods that are highly resistant to the presence of outliers and influential observations. The development and distribution of the algorithms created by this project will hasten the use of these important methodological developments by applied researchers in economics. Extending the theoretical work will eventually result in better empirical work, as the departures from underlying assumptions like normality and independence will no longer necessarily lead to a breakdown in esimtation techniques.