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香港科技大学 戴琳琳博士:Profile Likelihood Ratio Test for Semiparametric Families Under Case-control Sampling

([西财资讯] 发布于 :2018-04-02 )

光华讲坛——社会名流与企业家论坛第4857

 

 Profile Likelihood Ratio Test for Semiparametric Families Under Case-control Sampling

主讲人香港科技大学 戴琳琳博士   

主持人统计学院 林华珍教授

间:201843日(星期二)13:30-14:30

 点:利记娱乐网柳林校区弘远楼408会议室

主办单位统计研究中心 统计学院 科研处

 

主讲人概况: 

戴琳琳,现为香港科技大学数学学院博士,其研究方向是高维数据,非参数建模,统计机器学习,病例对照研究等。2013年在山东大学学报(工学版)发表1篇关于几类矩阵乘积在控制论中的应用的论文。2012年荣获山东大学国家科技创新基金项目一等奖;2017年还获得了香港科技大学研究旅行补助金(RTG) 

主讲内容:

Model discrimination is one of the most important subjects in statistics and machine learning research. A fundamental result established in (Chernoff, 1952) states that, for simple versus simple hypothesis, the type I and type II error probabilities for the likelihood ratio test decay exponentially at the same rate when there is no preference for the null or alternative hypothesis. This classical result was only recently extended to the generalized likelihood ratio test for composite versus composite hypotheses (Li, Liu and Ying, 2018), and the decay rates are called generalized Chernoff index.  These results are restricted to hypotheses of parametric families. It is unknown whether any such results would hold for hypotheses of semiparametric families. The main obstacle is the infinite dimension of the semiparametric models. Case-control studies arise from semiparametric models and are widely applied in biomedical studies and classification problems in machine learning research. We propose profile likelihood ratio test for semiparametric models and show that Chernoff's equal decay rates statement is indeed true for case-control studies.  Moreover, the explicit form of the generalized Chernoff index is obtained, along with the asymptotic distribution of the proposed test statistic. Simulation studies provide strong evidence in support of the theory. An application to spam email classification is demonstrated. Our results open the door towards the possibility that Chernoff's equal decay rates may be universal for a general class of profile likelihood ratio tests.


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