The Form, and Some Robustness Properties of Integrated Distance Estimators for Linear Models, Applied to Some Published Data Sets

摘要

A critical procedure for use in linear models is introduced and developed in some detail. It is based on a nonlinear analogue to the usual linear least squares procedure, more specifically, in the integrated distance between characteristic functions (densities) and their sample counterparts. Location and scale parameters are estimated simultaneously. The procedure depends on a user specified parameter which may be varied to determine the sensitively of the parameters and observational weights to such variation. A sensitivity analysis of this type is useful in isolating potential problems with the data or with the assumed model. When the procedure is employed with the user-oriented parameter held fixed, a robust procedure results. The statistical properties of this procedure are discussed in some detail. A number of illustrations, taken from the literature, are examined. (Author)