基于因变量抽样设计下线性回归模型的假设检验问题  

Hypothesis Testing in Linear Regression Model under Outcome-Dependent Sampling Design

作　　者：刁云霞 晏舒 丁洁丽[1] Yun Xia DIAO;Shu YAN;Jie Li DING(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.Chin;Zhuzhou Branch of China Unicom,Zhuzhou 412000,P.R.China)

机构地区：[1]武汉大学数学与统计学院,武汉430072 [2]中国联合网络通信有限公司株洲市分公司,株洲412000

出　　处：《数学学报（中文版）》2018年第6期1003-1020,共18页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11671310)

摘　　要：在许多大型队列研究中,采用节约成本并能提高效率的抽样机制至关重要,基于因变量的抽样设计正是这样一种有偏抽样机制.这种方法最大的优点在于：能够将资源集中在那些包含有更多的协变量与因变量关系信息的研究群体上.本文研究基于因变量抽样设计下的线性模型中回归方程显著性检验以及回归系数显著性检验问题.基于一种半参数经验轮廓似然的方法,我们分别为回归方程检验与回归系数检验提出了相应的检验统计量,获得了所提出检验统计量的渐近性质.通过模拟研究评估了所提出的检验方法在有限样本下的表现,并应用提出的方法分析了一个孕妇分娩的实际数据.cost-effective sampling design is desirable in large cohort studies due to the cost of measurement on expensive covariates. An outcome-dependent sampling （ODS） design is such a biased-sampling scheme which can improve efficiency by allowing researchers to oversample in the regions of most information. We study hypothesis testing in linear regression model under the ODS design. We propose a likelihood ratio statistic and a Wald statistic for testing the significance of the model, and a U statistic for testing the significance of regression parameter by applying a semiparametric empirical profile-likelihood method. We establish the asymptotic theory for the proposed test statistics. We conduct simulation studies to assess the finite-sample performance of the proposed tests. We illustrate the application of the proposed methods with a real data example.

关 键 词：有偏抽样 似然比检验 WALD检验 半参数经验似然 

分 类 号：O212.2[理学—概率论与数理统计]