ROBUST PREDICTION INTERVALS IN A REGRESSION SETTING

A lot of work has been done in the area of robust alternatives to least squares in a regression setting. This work has primarily focused on robust estimation of the parameters in a regression equation when the assumption of Gaussian errors has been relaxed. In a lot of real world situations estimation of parameters is just part of the problem of interest. It is often desired to predict a future dependent variable given the observed independent variables. The problem here is that if the desired level of prediction is large, say 90%, then the desired information lies in that part of the sample residuals which may contain outliers. This is true even if a robust regression procedure has been employed to estimate the parameters. In this study we intend to examine methods of predicting a future observation that are robust across a variety of situations involving errors that are symmetrically distributed. In other words, these procedures will provide prediction intervals that maintain the nominal coverage without being too wide.