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High-Dimensional Inference Based On The Leave-One-Covariate-Out Regularization Path, Xiangyang Cao

Theses and Dissertations

The increasingly rapid emergence of high dimensional data, where the number of variables p may be larger than the sample size n, has necessitated the development of new statistical methodologies. LASSO and variants of LASSO are proposed and have been the most popular estimators for the high dimensional regression models. However, not much work has focused on analyzing and summarizing the information contained in the entire solution path of the LASSO. This dissertation consists of three research projects that propose and extend the Leave-One-Covariate-Out(LOCO) solution path statistic to regression and graphical models.

In the first chapter, we propose a new …