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

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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.