ABSTRACT
In Chapters 2 and 3 we have emphasized the fact that the minimum distance estimation method based on disparities generates a rich and general class of estimators which includes the maximum likelihood estimator as a special case. Under differentiability of the model, the estimators are obtained by solving estimating equations of the form (2.39), or their analogs for the continuous case. In this chapter we will further explore the estimating functions under the weighted likelihood estimating equation approach to this problem. We will show that weighted likelihood estimating functions based on disparities also generate a very broad class of estimation processes containing the maximum likelihood score function as a special case. Under standard regularity conditions the above approach produces a class of asymptotically efficient procedures; in addition, many members of this class have very strong robustness features.
