This project will examine robust regression procedures for multiple linear regression and for nonlinear regression. In the first case, methods will be developed for the exact computations of least median of squares estimators. The theory and computation will be extended to the case when responses are arbitrarily censored; and bootstrap methods will be used to generate confidence intervals. In the case of nonlinear regression, the project will focus on determining the robustness of MM-estimation, which has been shown to be robust in the linear case. Predictions are often calculated from data using regression functions, which relate the value of the observation of interest to values of other features or attributes. Traditional computations used to derive the regression function itself are vulnerable to fairly rare but quite aberrant single data points (outliers). More robust alternative methods reduce the impact of individual unusual or bizarre data points; hence these methods should give more stable predictions.
