Inference of high-dimensional weak instrumental variable regression models without ridge-regularization

Statistical Seminar

Organizer：

Yunan Wu 吴宇楠

Speaker：

Xu Guo 郭旭

北京师范大学

Time：

Fri., 16:00-17:00, May 22, 2026

Venue：

C654, Shuangqing Complex Building A

Title：

Inference of high-dimensional weak instrumental variable regression models without ridge-regularization

Abstract:

Inference in instrumental variable regressions is challenging in modern applications involving many weak and high-dimensional instruments. A prominent line of work extends the classical Anderson–Rubin test to such settings through ridge regularization. In this paper, we show that ridge regularization is not essential for conducting inference that is robust to weak identification and heteroskedasticity. We propose a tuning-free jackknifed Anderson–Rubin quadratic-form test that is computationally simple and remains feasible even when the number of instruments exceeds the sample size. We further modify the Sup Score test by employing a Gaussian multiplier bootstrap to calibrate critical values under the null. This approach accommodates cross-instrument dependence and typically yields less conservative critical values. The resulting bootstrap-calibrated Sup Score test is particularly powerful when the firststage relationship between endogenous regressors and instruments is sparse. We establish asymptotic size control for both the tuning-free jackknifed Anderson–Rubin quadratic-form test and the bootstrap-calibrated Sup Score test under arbitrarily weak identification and heteroskedastic errors, and characterize their power properties under alternative hypotheses. Simulation studies and an empirical application demonstrate the practical advantages of the proposed methods relative to existing approaches.