Statistics ( IF 0.645 ) Pub Date : 2020-03-13 , DOI: 10.1080/02331888.2020.1739049 Weibin Zhong; Kepher H. Makambi; Ao Yuan
The empirical likelihood is a popular tool in statistics and many other fields, including regression analysis. It has the advantage of robustness against model specification and can incorporate side information to improve the estimation accuracy. There is vast literature on empirical likelihood incorporating various side information, mostly in the form of moment constraint(s). Here we study this method under two types of side information: symmetry and unimode of the underlying distribution. To our knowledge, incorporating such shape information formally via empirical likelihood has not been seen and is the goal of our study. Basic properties of the method are investigated, and extensive simulation studies are conducted to evaluate its performance and compared with the cases without such information. We found that the symmetry information can improve the variance of the estimator, while the unimode information has no such effect.