  In this paper a new family of minimum divergence estimators based on the
Bregman divergence is proposed, where the defining convex function has an
exponential nature. These estimators avoid the necessity of using an
intermediate kernel density and many of them also have strong robustness
properties. It is further demonstrated that the proposed approach can be
extended to construct a class of generalized estimating equations, where the
pool of the resultant estimators encompass a large variety of minimum
divergence estimators and range from highly robust to fully efficient based on
the choice of the tuning parameters. All of the resultant estimators are
M-estimators, where the defining functions make explicit use of the form of the
parametric model. The properties of these estimators are discussed in detail;
the theoretical results are substantiated by simulation and real data examples.
It is observed that in many cases, certain robust estimators from the above
generalized class provide better compromises between robustness and efficiency
compared to the existing standards.
