标题：A generalized semiparametric regression and its efficient estimation
作者：Lin, Lu; Liu, Lili; Cui, Xia; Wang, Kangning
作者机构：[Lin, Lu; Wang, Kangning] Shandong Technol & Business Univ, Sch Stat, Yantai, Peoples R China.; [Lin, Lu; Liu, Lili] Shandong Univ, Zhongtai Secur I 更多
通讯作者地址：[Lin, L]Shandong Technol & Business Univ, Sch Stat, Yantai, Peoples R China.
来源：SCANDINAVIAN JOURNAL OF STATISTICS
关键词：profile likelihood; semiparametric efficiency; semiparametric regression
摘要：We investigate a generalized semiparametric regression. Such a model can avoid the risk of wrongly choosing the base measure function. We propose a profile likelihood to efficiently estimate both parameter and nonparametric function. The main difference from the classical profile likelihood is that the profile likelihood proposed is a functional of the base measure function, instead of a function of a real variable. By making the most of the structure information of the semiparametric exponential family, we get an explicit expression of the estimator of the least favorable curve. It ensures that the new profile likelihood is computationally simple. Due to the use of the least favorable curve, the semiparametric efficiency is achieved successfully and the estimation bias is reduced significantly. Simulation studies can illustrate that our proposal is much better than the existing methodologies for most cases under study, and is robust to the different model conditions.