Resampling-Based Inference in High Dimensional Linear Models via Flipscore Tests

par Daniela Corbetta (IMT)

mardi 21 avr. 2026, 11:15 → 12:15 Europe/Paris

Salle E. Picard (1R2-129)

We consider inference in high-dimensional linear models where p>>n, focusing on testing individual regression coefficients and constructing confidence statements on the set of active predictors. Existing methods such as debiased lasso and ridge projection rely on approximate inversion of X’X and yield asymptotically valid inference, but may suffer from instability and loss of accuracy in finite samples, particularly under strong dependence.
We study an alternative approach based on the flipscore test, a resampling-based procedure that approximates the null distribution of score statistics via random sign-flipping. This method avoids explicit matrix inversion, is robust to variance misspecification, and accommodates dependence among predictors. However, its standard formulation requires a full-rank design and is not directly applicable when p>n.
To address this limitation, we propose a framework combining conditional resampling with preliminary variable selection. We investigate several strategies, including lasso-based screening, SVD-based dimension reduction, and stepwise selection, and analyze their impact on validity. Under suitable conditions on the selected model, we establish asymptotic validity of the resulting tests.
We further extend the approach to simultaneous inference on the full coefficient vector via multiple testing procedures, and exploit the resampling structure to obtain post-hoc bounds on the false discovery proportion that adapt to dependence. Simulation results highlight competitive error control and power compared to state-of-the-art methods.