《A SIMPLE AND EFFICIENT PROFILE LIKELIHOOD FOR SEMIPARAMETRIC EXPONENTIAL FAMILY》

Zhongtai Securities Institute for Financial Studies, Shandong University

Lu Lin教授莅临我院指导

2017年12月21日下午14点半，应广州大学经济与统计学院和岭南统计科学研究中心的邀请，Zhongtai Securities Institute for Financial Studies, Shandong UniversityLu Lin教授在行政东后座310作了题为A SIMPLE AND EFFICIENT PROFILE LIKELIHOOD FOR SEMIPARAMETRIC EXPONENTIAL FAMILY的讲座——暨“羊城讲坛”第二十三讲，旨在进一步提高年轻学者及研究生对研究的理解。此次讲座由崔霞副院长主持，相关专业的师生参加了此次讲座。本报告讲述提出了一种有效估计参数和非参数函数的剖面可能性。由于使用最少 在剖面似然过程中，成功地实现了半参数化效率，大大降低了估计偏差。

 

 

摘要：Semiparametric exponential family proposed by Ning et al. (2017) is an extension of the parametric exponential family to the case with a nonparametric base measure function. Such a distribution family has potential application in some areas such as high dimensional data analysis. However, the methodology for achieving the semiparametric efficiency has not been proposed in the existing literature. In this paper, we propose a profile likelihood to efficiently estimate both parameter and nonparametric function. Due to the use of the least favorable curve in the procedure of profile likelihood, the semiparametric efficiency is achieved successfully and the estimation bias is reduced significantly. Moreover, by making the most of the structure information of the semiparametric exponential family, the estima-tor of the least favorable curve has an explicit expression. It ensures that the newly proposed profile likelihood can be implemented and is computationally simple. Simulation studies can illustrate that our proposal is much better than the existing methodology for most cases under study, and is robust to the different model conditions.