Physical Sciences and Mathematics Commons^™

Distributed Quantile Regression Analysis And A Group Variable Selection Method, Liqun Yu

Arts & Sciences Electronic Theses and Dissertations

This dissertation develops novel methodologies for distributed quantile regression analysis

for big data by utilizing a distributed optimization algorithm called the alternating direction

method of multipliers (ADMM). Specifically, we first write the penalized quantile regression

into a specific form that can be solved by the ADMM and propose numerical algorithms

for solving the ADMM subproblems. This results in the distributed QR-ADMM

algorithm. Then, to further reduce the computational time, we formulate the penalized

quantile regression into another equivalent ADMM form in which all the subproblems have

exact closed-form solutions and hence avoid iterative numerical methods. This results in the

single-loop …