主 题：Profile Likelihood Ratio Test for Semiparametric Families Under Case-control Sampling
主办单位：统计研究中心 统计学院 科研处
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.