Semiparametric and Nonparametric Methods of Model Selection and Model Checking for Correlated Data

模型选择和模型检验是统计分析的基础。模型选择的主要目标是确定简约的拟合模型，以平衡模型拟合的增加与模型复杂性的增加;模型检查的主要目标是评估或测试拟议模型的有效性。大量的文献可用于独立的数据在这一研究领域。 然而，对于相关数据，只存在零散的工作，渐近理论在很大程度上尚未开发，主要是由于（1）缺乏丰富的模型，如多变量高斯模型，用于响应的联合分布，（2）即使这样的多变量分布族可用，联合似然的复杂性。这些障碍使得应用为独立数据或基于完全可能性开发的现有模型选择和模型检查程序极具挑战性，如果不是不可能的话。该项目通过开发一套用于相关数据的模型选择和模型检查的半参数和非参数工具来解决这一挑战，包括基于矩条件的模型检查程序，通过最近开发的二次推理函数和基于秩的估计方程;数据驱动的模型检查程序，允许灵活的替代方案并提高一般功率性能。本项目将对大样本理论和实际性能进行深入研究。议程上还包括相关研究问题，例如可能的模型错误指定下的秩回归的表征以及基于秩的模型选择算法的理论鲁棒性。相关数据经常出现在许多领域，例如生物医学和健康科学、经济学、社会科学和环境研究。这一工作将极大地丰富现有的模型选择和模型检验的方法和理论。调查员将开发统计学家和科学家可以轻松实施的计算软件包。该项目将为科学家提供新的和灵活的工具来分析高维相关数据。教育将是一个重要组成部分。研究结果将纳入各级统计课程。本科生和研究生，特别是那些来自代表性不足的群体，将被鼓励参加这个研究项目。

Model selection and model checking are fundamental to statistical analysis. The main objective of model selection is to identify parsimonious well-fitting models in order to balance the increase in model fit against the increase in model complexity; and that of model checking is to assess or test the validity of a proposed model. An enormous amount of literature is available for independent data in this research area. For correlated data, however, there exists only fragmented work and the asymptotic theory is largely undeveloped, mainly due to (1) the lack of a rich class of models such as multivariate Gaussian for the joint distributions of the responses, (2) the complexity of the joint likelihood even when such a multivariate family of distributions is available. These obstacles make it extremely challenging, if not impossible, to apply existing model selection and model checking procedures that were developed for independent data or based on full likelihood. This project addresses this challenge by developing a set of semiparametric and nonparametric tools for model selection and model checking for correlated data, including model checking procedures based on moment conditions via the recently developed quadratic inference function and rank-based estimation equations; data-driven model checking procedures that allow for flexible alternative and increase general power performance. The large sample theory and practical performance will be investigated in depth in this project. Also on the agenda are related research issues, such as the characterization of rank regression under possible model misspecification and the theoretical robustness properties of rank-based model selection algorithms.Correlated data frequently occur in many fields, such as biomedical and health sciences, economics, social sciences and environmental studies. This work will greatly enhance the available methodologies and theories for model selection and model checking. The investigator will develop computational packages that can be easily implemented by statisticians and scientists. This project will provide scientists with new and flexible tools for analyzing high-dimensional correlated data. Education will be an important component. The research results will be incorporated at different levels of statistical courses. Undergraduate and graduate students, especially those from underrepresented groups, will be encouraged to participate in this research project.