| This dissertation is concerned with the development and study of S-estimators, (')(beta), which are obtained as solutions to: (SIGMA) (pi)(,i) (psi) (y(,i) - x(,i)(')(beta))/(pi)(,i)s x(,i)('') = 0. The main objective of the (pi)-weights, (pi)(,i), is to make the estimator more resistant to outliers that occur at high leverage points.;The effects of collinearity on S-estimators are studied. It is concluded that collinearity can affect the S-estimators in much the same way as the least squares estimator. In addition, collinearity can cause the empirical influence curve (EIC) of the S-estimators to be unbounded.;A method to alleviate the effects of collinearity is proposed. Using simulation, it is shown that the combination of ridge regression and S-estimation can yield estimators with much better stability properties and bounded EIC.;Several forms of (pi)-weights are discussed and two new forms are proposed. All these forms are compared empirically. |
