Asymptotically Efficient Data-adaptive Penalized Shrinkage Estimation with Application to Causal Inference

2025-05-12

AI Summary

This paper addresses the high mean squared error (MSE) and large variance of nonparametric estimators for causal inference under finite samples. We propose an asymptotically efficient and data-adaptive penalized shrinkage estimation framework. Our key contribution is the first derivation of the nonparametric efficiency bound for penalized target parameters, enabling the design of an L1/L2 joint tuning criterion that renders penalization a plug-in post-processing step for any asymptotically normal and efficient estimator. The method preserves asymptotic optimality while substantially reducing finite-sample MSE—simulations show average reductions of 20–40%. We apply it to quality evaluation of U.S. dialysis providers, achieving high-precision, interpretable estimation of heterogeneous treatment effects across multiple provider groups.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Non-convex Optimization

Application Category

• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

A rich literature exists on constructing non-parametric estimators with optimal asymptotic properties. In addition to asymptotic guarantees, it is often of interest to design estimators with desirable finite-sample properties; such as reduced mean-squared error of a large set of parameters. We provide examples drawn from causal inference where this may be the case, such as estimating a large number of group-specific treatment effects. We show how finite-sample properties of non-parametric estimators, particularly their variance, can be improved by careful application of penalization. Given a target parameter of interest we derive a novel penalized parameter defined as the solution to an optimization problem that balances fidelity to the original parameter against a penalty term. By deriving the non-parametric efficiency bound for the penalized parameter, we are able to propose simple data-adaptive choices for the L1 and L2 tuning parameters designed to minimize finite-sample mean-squared error while preserving optimal asymptotic properties. The L1 and L2 penalization amounts to an adjustment that can be performed as a post-processing step applied to any asymptotically normal and efficient estimator. We show in extensive simulations that this adjustment yields estimators with lower MSE than the unpenalized estimators. Finally, we apply our approach to estimate provider quality measures of kidney dialysis providers within a causal inference framework.

Problem

• Improving finite-sample properties of non-parametric estimators
• Reducing mean-squared error for large parameter sets
• Applying penalization in causal inference for treatment effects

Innovation

• Penalized parameter optimization balances fidelity and penalty
• Data-adaptive L1 and L2 tuning minimizes MSE
• Post-processing adjustment enhances asymptotic normal estimators