2024/07/17 by Woonyoung Chang, Arun Kumar Kuchibhotla, Chang, Woonyoung +1
Engineering · Mathematics · #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2407.12278
openalex publication_date 2024/07/17 · openalex created_date 2024/10/25 · openalex updated_date 2026/07/28
We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as Z-functionals. Our approach combines self-normalized statistics with a test inversion principle, enabling honest inference under mild regularity conditions and without explicit variance estimation. To enhance geometric tractability, we propose novel split-normalized and Gateaux-normalized statistics that yield computationally feasible and interpretable confidence sets. A central contribution of this work is a comprehensive non-asymptotic width analysis: we derive high-probability upper bounds on the diameter of the proposed confidence sets, and quantify their proximity to Wald intervals under minimal assumptions. Applications to high-dimensional non-sparse linear and generalized linear regression demonstrate that our procedures achieve valid coverage and near-optimal rate of convergence for the width/diameter, while the classical methods including Wald and bootstrap fail.