High-dimensional statistical inference: model diagnostics, covariance matrix estimation and overdispersion data.

在过去的几十年里，随着信息技术的重大进步，海量和复杂结构的数据集在经济、金融、精算、基因组学和神经科学等许多领域变得越来越常见。然而，这些数据集的规模和复杂性在统计学习研究中带来了独特的理论和计算挑战。受现实世界问题的启发，该研究方案聚焦于高维特征选择问题，其中感兴趣的响应变量被建模为大量特征的一个小子集的函数。这项提议的目标是在这一前景光明的领域寻求一些新的方向。具体地说，我的研究计划的重点之一是开发模型诊断工具，以评估高维统计学习模型的特征选择和预测结果的可靠性。我的研究项目还涉及到高维数据中的偏相关、零膨胀和过度离散的建模，这都使得特征选择问题变得更加具有挑战性。此外，这项建议还涉及精算统计前沿领域的研究课题。该建议的一部分集中于用于非寿险保费预测的高维特征选择技术，该技术联合建模保单的预期索赔损失和相关风险分散的结构。我提出的研究计划将解决高维学习模型中尚未解决的统计问题，并为更广泛的统计受众感兴趣的实际问题提供解决方案。然后，建议的方法可以立即用于解决生物信息学、经济学、工程学和神经科学等领域的科学问题。我在保险费预测方面的工作也可能对现代精算方法的发展产生影响，并对许多商业应用做出重大贡献。

With the major advances in information technology in the past few decades, datasets of massive size and complex structures are becoming increasingly common in many fields such as economics, finance, actuarial science, genomics and neuroscience. Yet that size and complexity of these datasets introduces unique theoretical and computational challenges in statistical learning research. Motivated by real-world problems, this research proposal focuses on the high-dimensional feature selection problems where a response variable of interest is modeled as a function of a small subset of a large number of features. The goal of this proposal is to pursue some new directions in this promising area. Specifically, one of the emphases of my research program is on developing model diagnostic tools to evaluate the reliability of feature selection and prediction results from the high-dimensional statistical learning models. My research program also concerns the modeling of partial correlation, zero-inflation and overdispersion in high-dimensional data, which all make the feature selection problem even more challenging. Additionally, this proposal also involves research topics in the frontiers of actuarial statistics. A part of this proposal focuses on the high-dimensional feature selection techniques for non-life insurance premium prediction, which jointly model the structure of the expected claim loss and associated risk dispersion of an insurance policy. My proposed research program will address unresolved statistical issues in high-dimensional learning models, and offer solutions to practical problems of interest to a broader statistical audience. The proposed methods could then immediately be used to solve scientific problems in areas such as bioinformatics, economics, engineering, and neuroscience. My work on the insurance premium prediction could also have impacts on the developments of modern actuarial methods and contribute significantly to many business applications.