Abstract:
|
A new method for robust regression based on unimodal density estimation is described. We assume only that the error density is smooth, unimodal, and symmetric. We estimate the regression function (i.e., the coefficients of a parametric regression function, or the spline basis function coefficients) and the error density simultaneously using profile methods. That is, for any coefficient vector, we can compute the residuals, then for those residuals, we estimate a density using a least-squares criterion. We search the coefficient vector space for the solution that minimizes the criterion. This produces both an estimate for the regression function, and an estimate for the error density, which can be used for inference. Because the estimate can be either light- or heavy-tailed, this method is quite robust. We show that the method is related to Huber's M-estimation and give asymptotic properties of the regression function estimator.
|
ASA Meetings Department
732 North Washington Street, Alexandria, VA 22314
(703) 684-1221 • meetings@amstat.org
Copyright © American Statistical Association.