【作者】 赵慧秀；

【导师】 郭建华；

【作者基本信息】 东北师范大学 ， 概率论与数理统计， 2009， 博士

【摘要】 在很多应用中，我们可以合理的认为来自于同一个团(cluster)的数据是可交换的。实际上，在一些团型抽样调查(cluster sample surveys)中、畸形学试验(teratological experiments)中、眼科及耳鼻喉科研究(ophthalmological and oto-laryngologic studies)中和其它的临床试验中，经常出现可交换的两值数据。本文的主要目的就是给出可交换的两值数据的统计分析的新方法。为了解决可交换的两值数据中的统计问题，我们先给出了一类最优无偏估计方程和关于一般估计方程的解的相合性和渐近正态性的一些理论结果，并且进一步给出了当估计方程中出现缺失数据时，利用一种迭代算法来解估计方程。我们把这种算法称作AU算法。由于AU算法在以下两步中迭代：在A步中，利用完全数据函数的条件期望的近似值来代替完全数据的函数，在U步中，用一个显示表达式来更新待估参数。所以此算法使得计算带有缺失数据的估计方程的求解具有了可行性和简单性。关于此算法的收敛性和由此算法得到的估计方程解的大样本性质，我们也给了一些理论结果。而且我们还给出了AU算法中关于A步中条件期望的一种的近似形式。基于我们得到的有关估计方程的这些理论结果，我们利用成对似然的方法(pairwise likelihood procedure)给出了一组近似最优无偏估计方程来计算带有随机簇(random cluster sizes)的可交换的两值数据的均值参数和相关参数。然后把这一方法应用到发育毒性数据分析中。通过模拟，我们得到了对于可交换的两值数据来说，我们的这一方法比GEE方法产生的结果好。当可交换的两值数据中出现缺失数据时，我们把成对似然的方法和AU算法结合起来。我们把这一方法应用到来自于繁殖毒性研究中的一组数据。通过模拟结果，也可看出我们的这一方法是有效的，而且此方法产生的结果也比忽略了带有缺失数据的个体的完全情形分析的结果好。更多还原

【Abstract】 In many applications, it is reasonable to expect exchangeability to model the datafrom the same cluster. In fact, exchangeable binary data are commonly encounteredin cluster sample surveys, teratological experiments, ophthalmological and otolaryngologicstudies, and other clinical trials. This dissertation aims to propose some newstatistical methods for exchangeable binary data analysis.In order to solve the problem, we first present a general form of optimal unbiasedestimating equations and some results for the consistency and the asymptotic normalityof the solutions to general estimating equations. Then we present an iterative algorithmfor solving estimating equations in the presence of missing data. The algorithm iscalled the AU algorithm. It makes the computation very feasible and simple because ititerates between two steps: an A-step, in which the functions of the complete data arereplaced by the approximate values of their conditional expectations, and a U-step inwhich the parameters are updated using a closed-form expression. Theoretical resultsare obtained establishing convergence properties of the algorithm and the large sampleproperties of the estimators produced by the algorithm. Moreover, we give a generalform of the approximations of the conditional expectations in the A-step of the AUalgorithm.Based on the theories of estimating equations we have obtained, we use a pairwiselikelihood procedure to give a set of approximately optimal unbiased estimatingequations for estimating the mean and variance parameters for the exchangeable binarydata with random cluster sizes. An application to developmental toxicity data analysisis given. Simulation results show that our procedure performs better than the GEEprocedure for the exchangeable binary data.When the exchangeable binary data involve missing data, we combine the pairwiselikelihood procedure with the AU algorithm. An application is made to a data setfrom a reproductive toxicity study. Simulation results show that our method is valid and performs better than the complete-case analysis which ignores the subjects withmissing data.更多还原