ABSTRACT 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.

中文翻译：

---

使用带形状信息的经验似然的半参数回归

摘要 经验似然是统计学和许多其他领域（包括回归分析）中的流行工具。它具有对模型规范具有鲁棒性的优点，并且可以结合边信息来提高估计精度。有大量关于包含各种辅助信息的经验可能性的文献，主要是矩约束的形式。在这里，我们在两种类型的边信息下研究这种方法：基础分布的对称性和单模态。据我们所知，还没有看到通过经验可能性正式合并这些形状信息，这也是我们研究的目标。研究了该方法的基本特性，并进行了广泛的模拟研究以评估其性能并与没有此类信息的情况进行比较。