随着科技的发展, 日益多样化和精细化的试验方法使得我们采集到的统计数据从种类上和数量上都日趋复杂和繁多. 如何有效地将额外的数据信息与我们所研究的目标样本相结合, 以提高统计推断的效率已成为当今统计研究中的一个热门的话题. 利用辅助信息是目前信息整合方法中的常用手段之一. 本篇论文针对两类统计数据：一元删失数据(属于不完全数据的一种) 和多元相关性数据(完全数据), 分别使用常系数加法危险率回归模型(Constant-coefficient additive hazards model) 和边际模型(Marginal model) 来研究辅助信息对提高模型参数估计功效的作用. 论文的主要内容分为如下四个部分. 在第一部分中(论文的第一章), 我们分别介绍了辅助信息的研究背景; 论文所涉及的两类数据: 右删失数据和相关性数据; 两类回归模型: 加法危险率模型和边际模型; 以及本研究会涉及到的两种统计方法: 经验似然方法和广义矩估计方法. 在第二部分(论文的第二章) 中, 我们将给出常系数加法危险率模型的带辅助信息的参数估计方法, 加法危险率模型是生存分析中非常重要的一类回归模型, 它可用于探索潜在的风险因子与失效时间(Failure time) 之间的关系. Lin 和Ying [42] 基于一种伪得分方程给出了常系数加法危险率模型的参数估计的显示表达式. 受到Huang 等[31] 的启发, 我们将??*–生存概率作为辅助信息, 并将其与Lin 和Ying [42] 给出的得分方程相结合, 利用经验似然理论, 给出常系数加法危险率模型参数的更为有效的估计量. 文中, 我们指出所提估计量的渐近正态性, 从理论角度证明了所提方法在功效上的优势. 同时, 我们通过一系列的随机模拟研究和一组艾滋病的实例(ACTG 175) 验证了所提方法在有限样本下的可行性. 在第三部分(论文的第三章和第四章) 中, 我们研究了带辅助信息的边际模型的参数估计方法. 边际模型是处理带有相关性数据的一种常用工具. 二次推断函数(Quadratic Inference Function, QIF) 方法是估计该模型中未知参数的一种较为有效的方法. 在这部分, 我们首先给出一种新的形式的辅助信息, 然后分别借助广义矩估计(Generalized Method of Moments, GMM) 与经验似然理论, 将提出的辅助信息运用到边际模型的 QIF 估计过程中, 得到该模型中未知参数的两种功效更高的估计量. 此外, 我们分别证明了这两种估计量的渐近正态性以及模型参数的检验统计量的大样本性质, 得到了加入辅助信息的确可以提高模型参数功效的结论. 估计量的极限分布表明由GMM 与经验似然方法得到的带有辅助信息的参数估计量的渐近性质相同. 最后, 我们通过一系列的随机模拟试验和一个关于中学生成绩的实例, 检验了所提估计方法在有限样本下的可行性. 在第四部分(论文的第五章), 我们对论文研究的主要内容和所得的结论做了总结, 并对今后的研究方向和思路做了简要的说明.

With the rapid development of technology and science, methods of studies become increasingly diversity and accurate, which makes the type and quantity of data we collect become more complex and multiple. How to improve the efficiency of statistical inference by incorporating some external information into our object population effectively has become a popular topic in statistics. Using the auxiliary information is one of the common methods for combing different sources of information. This paper focus on two kinds of data: the one dimensional censored data (one type of incomplete data) and multivariate dimensional correlated data (complete data) and apply the constant-coefficient additive hazards model and marginal model respectively to explore how to improve the efficiency of parameter estimation by the auxiliary information. This paper includes four main parts. In the first part (the first chapter), we introduce the background of auxiliary information; the two types of data related to our research which includes the right censored data and the correlated data; two kinds of regression models–the additive hazards model and the marginal model; and two methods that are related to our research, the empirical likelihood method and the generalized method of moments method. In the second part (the second chapter), we propose the estimation method of constant-coefficient additive hazards model with auxiliary information. The additive hazards model is one of the most important regression models in survival analysis, which can be used to explore the relationship between the potential factors and the failure time. In this chapter, we also demonstrate the asymptotic normal of the proposed estimator and illustrate the advantage of the new estimator from the theoretical aspect. At the same time, we test the performance of the proposed method by a series of simulation studies and a real data about the AIDS. In the third part of this paper (the third and the fourth chapters), we study the parameter estimation method with auxiliary information of the marginal model. Marginal model is a common instrument of analyzing the correlated data. The Quadratic Inference Function (QIF) method is an efficient estimation method to that model. In this part, we proposed a new type of auxiliary information firstly. Then we apply the auxiliary information into the procedure of QIF estimation by the generalized method of moments (GMM) and empirical likelihood theory respectively. Thus getting two more efficient estimators. In addition, we demonstrate the asymptotic normal and large sample properties of the new estimators and the test statistics, which help us get the conclusion that combing the auxiliary information is of help to improve the efficiency of parameter estimator. The limit distribution of the proposed estimators indicates that the asymptotic properties of the GMM and empirical likelihood estimator with auxiliary information are of the same. Finally, we test the performance of the new estimators by a series of simulation studies and a real data about the score of middle school students. In the fourth part (the fifth chapter), we summary the main content and the conclusions of this paper, and make a brief description about the thought of research in the further.