Omniscience in Adversarial Causal Inference: Implications for Balancing Estimators of Average Treatment Effects Open Access

Abstract

In the realm of causal inference, covariate imbalance is a major challenge to achieving unbiased causal estimations. Balancing, the idea that we can put different weights on observations to minimize covariate imbalance, is one of many methods that have been developed and widely used. The criterion with which weights are assigned is connected to minimaxity--minimizing maximum squared-error loss. Yet, balancing estimator considers an adversarial that knows the randomization of treatment, thereby rendering the adversary extremely powerful. Using the idea of minimax-Bayes, we develop an average treatment effect estimator that only knows the distribution of treatments, not realized treatments. Compared to balancing estimator, our minimax-Bayes estimator has a less omniscient adversary, and we investigate whether it results in better average treatment effects estimation. 

Table of Contents

1 Introduction…………………………………………………………….……………….….1

2 Framework…………………………………………………………….……………….…...2

2.1 The Estimand………………………………………………………………………………2

2.2 The Estimator……………………………………………………………………………...3

2.2.1 Minimax Estimators…………………………………………………………………...4

2.2.2 Inverse Probability Weighting……………………………………………………….5

2.3 Least Favorable Distribution…………………………………………………………...6

3 Results………………………………………………………………………………………..6

3.1 Analytical Derivation…………………………………………………………………….6

3.2 Numerical Solution……………………………………………………………………….9

3.3 Least Favorable Curves and Least Favorable Distribution……………………..10

4 Empirical Performance………………………………………………………………...11

References………………………………………………………………………….............14

About this Honors Thesis

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School	Emory College
Department	Quantitative Theory and Methods
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Statistics Biology, Biostatistics
Keyword	Bayesian Statistics Nonparametric Statistics Causal Inference
Committee Chair / Thesis Advisor	Hirshberg, David , Emory University
Committee Members	O'Connell, Stephen , Emory University McAlister, Kevin, Emory University

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