Semiparametric Models for Correlated Data: The Quadratic Inference Function Approach

相关数据的半参数模型：二次推理函数方法

• 批准号: 0103513
• 负责人: Annie Qu
• 金额: $ 7.91万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-15 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0103513&HistoricalAwards=false
• 关键词: Semiparametric; Models; Correlated; Data; Quadratic

This research focuses on a new statistical method for the analysis of correlated data, the quadratic inference function (QIF) approach (Qu, Lindsay & Li 2000). The QIF is built on a semiparametric framework defined by a set of mean zero estimating functions, but differs from the standard estimating function approach in that there are more equations than the number of unknown parameters. The QIF has advantages compared to the estimating function approach, such as not requiring the specification of the likelihood function. It also overcomes limitations of the estimating function approach such as a lack of objective functions and likelihood functions for testing. One of the main goals of the proposed project is to explore the QIF for robustness with respect to the consistency of estimators when mean zero assumptions are not satisfied. A second goal focuses on the missing data problem, which occurs often in longitudinal data. Testing whether missing data are ignorable is still a challenging problem in general. The goodness-of-fit test for the QIF appears to be a valid test for nonignorable missing data. The third goal is to test order restricted alternative hypotheses for correlated data using the QIF. Current existing testing tools are not satisfactory and are mainly based on the likelihood function for parametric models, and therefore are not applicable for correlated data where the likelihood function is difficult to formulate. The QIF is related to the empirical likelihood (Owen, 1988) which is popular for nonparametric models. The proposed project also illustrates the Edgeworth expansion of QIF and explores how to apply the bootstrap strategy to improve testing accuracy for small samples of correlated data.This research will have a significant impact and many applications in biostatistics, econometrics, and the environmental and social sciences where correlated data arise often. In particular, the QIF method substantially improves the estimation of regression parameters in generalized estimating equation settings (Liang & Zeger, 1986). Considering a real world example of air pollution for health impact assessment, even a slight difference in the regression parameter estimates can have a major impact on our health and environmental policies. Further, it is also the first effort to connect the generalized method of moments (Hansen, 1982) in econometrics to estimating functions in the statistics field. It attempts to answer a question frequently asked by econometricians: how to choose the most informative moment conditions with the lowest dimension possible. The research will also serve an educational purpose through developing a new course on longitudinal data and training of graduate students.

本研究主要探讨一种分析相关资料的新统计方法--二次推断函数法(QIF)(Qu，Lindsay&Amp；Li，2000)。QIF建立在由一组均值零估计函数定义的半参数框架上，但与标准估计函数方法不同的是，方程的数量多于未知参数的数量。与估计函数方法相比，QIF方法具有优势，例如不需要指定似然函数。它还克服了估计函数方法的局限性，如缺乏用于测试的目标函数和似然函数。该项目的主要目标之一是探索当均值为零的假设不满足时，关于估计量一致性的QIF的稳健性。第二个目标集中于丢失数据的问题，该问题经常发生在纵向数据中。测试丢失的数据是否可以忽略总体上仍然是一个具有挑战性的问题。对于不可忽略的缺失数据，QIF的拟合优度检验似乎是一种有效的检验。第三个目标是使用QIF检验相关数据的顺序限制替代假设。现有的检验工具不能令人满意，主要是基于参数模型的似然函数，因此不适用于似然函数难以表示的相关数据。QIF与经验似然(Owen，1988)有关，而经验似然在非参数模型中很流行。该项目还展示了QIF的Edgeworth展开，并探索了如何应用Bootstrap策略来提高相关数据的小样本测试精度。这项研究将在经常出现相关数据的生物统计学、计量经济学以及环境和社会科学中产生重大影响和许多应用。特别是，QIF方法大大改进了广义估计方程设置中回归参数的估计(Leung&Amp；Zeger，1986)。考虑到用于健康影响评估的空气污染的真实例子，即使回归参数估计中的微小差异也可能对我们的健康和环境政策产生重大影响。此外，这也是首次将计量经济学中的广义矩方法(Hansen，1982)与统计领域中的估计函数联系起来。它试图回答计量经济学家经常提出的一个问题：如何以尽可能低的维度选择最具信息量的时刻条件。这项研究还将通过开发一门关于纵向数据和研究生培训的新课程来服务于教育目的。