Locally efficient semiparametric estimators for generalized skew-elliptical distributions

We consider a class of generalized skew-normal distributions that is useful for selection modeling and robustness analysis and derive a class of semiparametric estimators for the location and scale parameters of the central part of the model. We show that these estimators are consistent and asymptotically normal. We present the semiparametric efficiency bound and derive the locally efficient estimator that achieves this bound if the model for the skewing function is correctly specified. The estimators that we propose are consistent and asymptotically normal even if the model for the skewing function is misspecified, and we compute the loss of efficiency in such cases. We conduct a simulation study and provide an illustrative example. Our method is applicable to generalized skew-elliptical distributions.