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Minimax rates for heterogeneous causal effect estimation.

Edward H Kennedy1, Sivaraman Balakrishnan1,2, James M Robins3

  • 1Department of Statistics & Data Science, Carnegie Mellon University.

Annals of Statistics
|April 2, 2025
PubMed
Summary
This summary is machine-generated.

This study establishes the minimax rate for estimating heterogeneous causal effects (CATEs) and introduces a novel local polynomial estimator. The findings provide theoretical guarantees for optimal CATE estimation in nonparametric models.

Keywords:
causal inferencefunctional estimationhigher order influence functionsnonparametric regressionoptimal rates of convergence

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Estimating heterogeneous causal effects (CATEs) is crucial for understanding treatment and policy variations.
  • Existing methods for CATE estimation lack a developed minimax theory of optimality.
  • Optimal convergence rates and estimators for CATEs remain open problems in causal inference.

Purpose of the Study:

  • To derive the minimax rate for CATE estimation in Hölder-smooth nonparametric models.
  • To introduce a new local polynomial estimator that achieves minimax optimality under specific conditions.
  • To develop a minimax theory for CATE estimation.

Main Methods:

  • Derivation of a minimax lower bound using a localized method of fuzzy hypotheses.
  • Construction of lower bounds by combining nonparametric regression and functional estimation techniques.
  • Development of a local polynomial R-Learner based on modified influence function methods.

Main Results:

  • The study derives the minimax rate for CATE estimation.
  • A novel local polynomial estimator is proposed and shown to be minimax optimal under defined conditions.
  • The derived minimax rate exhibits a non-standard elbow phenomenon and interpolates between regression and functional estimation rates.

Conclusions:

  • This work provides the first minimax lower bound for CATE estimation.
  • The proposed local polynomial estimator offers a theoretically optimal approach for CATE estimation.
  • The findings highlight the hybrid nature of CATE as an estimand, bridging nonparametric regression and functional estimation.