WITHDRAWN: Non-parametric Counterfactual Regression with Applications in Causal Inference with Dependent Data

Music City Center 

Series regression estimates the conditional mean of a response variable by regressing it on features derived from basis functions evaluated at covariate values. Ordinary least squares (OLS)-based series estimators achieve minimax rate optimality but impose stringent assumptions on basis functions. To address this, prior work introduced the Forster-Warmuth (FW) learner, which relaxes these conditions using a unified pseudo-outcome framework to minimize bias from nuisance function estimation, achieving minimax rates under mild assumptions. While these results relied on an i.i.d. sample condition, we extend the FW framework to dependent data settings, including time series and spatial structures. Our analysis shows that under specific dependence conditions, the ℓ2 error rate aligns with the i.i.d. case, preserving minimax optimality. This extension broadens the applicability of FW-inspired methods to high-dimensional and structured data. We demonstrate its utility by estimating dose-response curves for continuous treatments under both unconfounded and confounded scenarios. We model air pollution's immediate effects on heart attack rates to identify actionable public health insights.

Series regression

Forster-Warmuth (FW) learner

Minimax rate optimality

Dependent data

Dose-response curves

Air pollution and heart attack rates 

IMS