PhD Seminar: Discovering Sparsity Structure in Nonparametric Regression: An Adaptive Overlapping Group Lasso Approach with Application to Doubly Robust DiD

Discovering Sparsity Structure in Nonparametric Regression: An Adaptive Overlapping Group Lasso Approach with Application to Doubly Robust DiD

We propose a consistent variable selection procedure for nonparametric regression that avoids imposing restrictive functional form assumptions. Using tensor-product basis expansions to approximate unknown functions, we develop a novel adaptive overlapping group Lasso (AOGLasso) estimator to identify relevant covariates. To address the associated computational challenges, we implement an efficient optimization strategy adapted from the alternating direction method of multipliers (ADMM), combined with a preliminary variable screening step. We establish the asymptotic properties of this procedure and show that it consistently recovers the true set of covariates. The method is primarily motivated by the need for robust estimation of nuisance parameters in high-dimensional causal inference. We demonstrate its utility within doubly robust difference-in-differences frameworks, where it effectively mitigates the curse of dimensionality while maintaining robustness against functional misspecification. Simulation studies confirm the approach’s finite-sample performance.