A0381
Title: Statistical properties of a flexible regularized estimating equation formulation
Authors: Yue Zhao - University of York (United Kingdom) [presenting]
Abstract: A central topic in high-dimensional statistics facing very many variables is regularisation, which seeks to retain only a few impactful variables in the estimated model. While regularised optimisation formulation has been well studied, much less has been said about the regularised estimating equation. The proposal is to formulate the zero root of a regularised estimating equation as the fixed point of a proximal operator specified by the regulariser. In this way, finding the zero root is translated into finding the fixed point of the proximal operator, for which many efficient algorithms exist. In addition, the said proximal operator is itself a simple convex problem and often admits closed-form solutions, even for more complex regularizers such as the non-convex (group) SCAD and MCP. The statistical properties of the solutions to the algorithm are presented, such as their variable selection consistency, in the non-asymptotic, high-dimensional regime. These solutions are shown to behave similarly to those from a comparable optimization formulation. Numerical studies also demonstrate the computational advantage of our algorithm.
