Mathematical Sciences: Regression Quantile Methods and Asymptotic Statistical Theory

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The research objectives involve extending the regression quantile methodology and developing new asymptotic approaches to cases of large parametric dimension. Methodological aims include the following: (a) to develop adaptive estimators in the linear regression model which are fully efficient under any assumption on the error distribution, (b) to define and investigate outlier detection prodedures and to apply them for providing resistance to the presence of outliers and influential observations, (c) to investigate the performance of the regression quantile algorithm, and (d) to obtain robust analyses for nonlinear regression models and for structural models in econometrics. Aims for new asymptotic approaches include the following: (a) to obtain appropriate asymptotic results for the regression quantile methodology in linear models, (b) to study standard and robust methods for analyzing structural models, and (c) to investigate the adequancy of such asymptotic approximations for real and simulated data sets. This research in the field of statistics is to develop and analyze robust econometric procedures. Robust statistical methods are procedures that work well even when applied to situations where the underlying assumptions in the mathematics are unrealistic and do not hold. Since mathematical models of the economy are approximations of very complex systems for which the true underlying mathematical representation may well be unknown, and since data brings measurement error and other uncertainty with its very creation, it is advantageous to have statistical techniques that are known to perform well under adverse conditions.