Dimension-agnostic inference for M-estimation
Speaker: Kenta Takatsu
Abstract: Many statistical applications can be framed as the solution of stochastic optimizations whose objective function is estimated from data. This framework, widely known as M-estimation, includes maximum likelihood estimation, functional estimation, regression, and classification. Classical inferential methodologies for M-estimation often rely on strong assumptions about the underlying distribution as well as the asymptotic properties of the estimator. As a result, there is a severe shortage of inferential tools for high-dimensional settings. A simple method is proposed for constructing a confidence set for M-estimation, which remains valid without assumptions about the dimension of data. The proposed confidence set is based on a sample-splitting procedure, and conditions are provided under which its diameter converges at an optimal rate. Furthermore, the proposed method is applicable to non-standard problems where the inference has been notoriously difficult.