广义定序回归模型的高维统计推断及其应用

定序数据是一类在经济金融、社会科学等领域广泛存在的数据类型。在大数据时代，具有定序响应变量的复杂面板数据以及具有高维协变量的定序响应变量数据已经随处可见。人们希望从这些复杂的数据中提取有用的信息，为不同学科领域的科学分析和决策提供支持。但是，经典的定序回归模型方法还存在很多的缺点，包括无法直接进行固定效应定序面板数据模型分析、无法进行定序回归模型的高维变量选择、无法刻画多组别定序响应变量的方差异质性等，而且这些缺点在现有定序回归模型的分析框架下是无法克服的。本项目拟提出广义定序回归模型的分析框架，克服经典定序回归模型存在的缺点，为定序面板数据模型的统计推断、定序回归模型的LASSO-类高维变量选择、以及协变量校正下的定序响应变量的比较等科学问题提供严谨的统计分析方法。项目还将开展以信用评级为典型代表的应用研究。

Ordinal data is a kind of data type widely existing in the fields of economy, finance, social science and so on. In the era of big data, complex panel data with ordinal response and ordinal response variable data with high dimensional covariates have been widely seen. People hope to extract useful information from these complex data and provide support for scientific analysis and decision-making in different disciplines. However, there are still many shortcomings in the classical ordinal regression model, including the inability to directly analyze the fixed effect ordinal panel data model, the inability to conduct high-dimensional variable selection in the ordinal regression model, the inability to model the variance heterogeneity of multiple groups of ordinal response variables, and these shortcomings cannot be overcome in the analysis framework of the existing ordinal regression model. This project will put forward the analysis framework of the generalized ordinal regression model, overcome the shortcomings of the classical ordinal regression model, provide rigorous statistical analysis methods for scientific problems such as statistical inference of the ordinal panel data model, LASSO-type high dimensional variable selection of the ordinal regression model, and the covariates-adjusted comparison of groups with ordinal responses. Moreover, this project will also carry out application research with credit rating as a typical representative.