Multiple Imputation Inferences with Public-Use Data Files and Frequentist Properties of Bayesian Procedures

DMS 9626691梦这是一个关于多重归责方法论的综合研究项目。多重归因方法是处理抽样调查中常见和复杂的无回答问题的最有效的推理方法，特别是那些产生许多用户共享的公共使用数据文件的抽样调查。多重归责框架是在贝叶斯视角下建立的，主要是因为贝叶斯方法为构建包含所有可用信息的复杂归责模型提供了一个连贯和灵活的通用框架。然而，公共使用的数据文件被设计成由许多用户共享的事实要求用于创建多个推算和用于分析多个推算的数据集的过程必须具有良好的频率特性。因此，多重归因的研究和使用突出了贝叶斯和频率主义视角的融合，从而在这两个视角的交叉点上提出了许多具有挑战性和耐人寻味的研究问题。为了有效地解决这些问题，本研究同时在两个层面上进行。在一般水平上，该研究检验了贝叶斯过程的新的稳健频率特性。在具体的层面上，研究了这些性质在多重归因中的应用，重点是构建新的程序以及在更一般的条件下证明现有程序的合理性。具体的主题包括不相容的多重推论下的置信度有效性，后验预测p值的频率特性，以及具有单一观测无偏先验的无偏推算。这项研究研究了重要而复杂的无回答问题，这是所有抽样调查固有的问题。无反应引起的最严重的问题是无反应偏见，即无反应的人与有反应的人在系统上是不同的。在社会、经济和统计文献中，系统的差异已经被反复记录，例如，在自我报告收入方面。如果这种偏见得不到纠正，只使用答复者的回答，很可能会得到一个非常扭曲的基本人口特征(例如，家庭平均年收入)的图景。纠正这种系统性的扭曲，特别是对大型公共数据文件来说，是一项非常复杂和艰巨的任务。基本任务是通过使用非受访者的现有信息(例如，人口统计信息)来预测他们的缺失值，从而减少无响应偏差。由于我们的预测具有不确定性，我们需要不止一个预测，即归罪，才能诚实地显示不确定性。有了一个以上的归因，单个用户就可以直接估计由于无响应而造成的信息损失，从而只使用标准的完整数据分析程序就可以获得有效的统计推断。显然，归责模型的好坏直接影响到后续统计分析的质量。这项研究的一个主要目的是为构建归责模型提供更好和更灵活的方法；对公共使用数据文件的分析通常对我们的社会产生深远影响，这一事实突显了这种研究的意义，因为这些分析得出的结论通常被用来回答经济学、教育学、人口学、公共卫生和政策、社会学、政治学等领域的问题。这项研究的另一个目的是探索在其他内容领域利用为多重归因于缺失数据问题而开发的方法的可能性，例如处理紫外线辐射测量中缺失观测值的问题，而紫外线辐射测量对于获取臭氧消耗造成的全球大气变化至关重要。

DMS 9626691 Meng This is a comprehensive research program on multiple imputation methodology. Multiple imputation methodology is the most effective inferential method available for handling the common and complex problem of nonresponse in sample surveys, especially those that produce public-use data files shared by many users. The multiple imputation framework was established under the Bayesian perspective, mainly because the Bayesian approach provides a coherent and flexible general framework for constructing sophisticated imputation models that incorporate all available information. However, the fact that the public-use data files are designed to be shared by many users requires that the procedures used for creating multiple imputations, and for analyzing the multiply-imputed data sets, must have good frequentist properties. Thus, the study and use of multiple imputation highlights and requires the melding of the Bayesian and frequentist perspectives, thus posing many challenging and intriguing research problems at the intersection of these two perspectives. To effectively tackle these problems, this research is conducted simultaneously at two levels. At the general level, the research examines new robust frequentist properties of Bayesian procedures. At the specific level, the research studies the use of these properties in multiple imputation, with a focus on constructing new procedures as well as justifying existing ones under more general conditions. Specific topics include confidence validity under uncongenial multiple imputation inferences, frequentist properties of posterior predictive p-values, and unbiased imputations with single observation unbiased priors. This research studies the important and complicated problem of nonresponse, a problem inherent to all sample surveys. The most serious problem caused by nonresponse is nonresponse bias, that is, those people who do not respond are systematically different from those who do respond. Su ch systematic differences have been repeatedly documented in the social, economic, and statistical literature, for example, on self-reporting of income. If the bias is not corrected and only the answers from respondents are used, a very distorted picture of the characteristics (e.g., average annual income of households) of the underlying population is likely to be obtained. Correcting for such systematic distortion, especially for large public-data files, is a very complex and demanding task. The basic task is to reduce the nonresponse bias by using available information (e.g., demographic information) on the nonrespondents to predict their missing values. Since we have uncertainty in our prediction, we need more than one prediction, i.e. imputation, to honestly display the uncertainty. With more than one imputation, it becomes straightforward for an individual user to estimate the loss of information due to nonresponse and thus obtain valid statistical inference using only standard complete-data analysis procedures. It is obvious that the quality of the imputation model has direct impact on the quality of the subsequent statistical analyses. A main aim of this research is to provide better and more flexible methodologies for constructing imputation models; the significance of such a research is highlighted by the fact that the analyses of public-use data files typically have a profound impact on our society because the conclusions from these analyses are typically used to answer questions in economics, education, demographic studies, public health and policy, sociology, political science, among others. Another aim of this research is to explore the possible use of the methodologies developed for multiple imputation to missing-data problems in other content areas, such as the problem of handling the missing observations in ultraviolet radiation measurements, which are crucial for accessing global atmospheric changes due to ozone depletion.