Modelling hetegeneous treatment effects by quantitle local polynomial decision tree and forest

TL;DR

This paper introduces a novel method combining quantile classification with local polynomial estimation in decision trees and forests to improve inference on heterogeneous treatment effects, leveraging classical statistical properties.

Contribution

It proposes the quantile local linear causal tree and forest, integrating quantile-based partitioning with polynomial estimation for better treatment effect modeling.

Findings

Provides constructible confidence intervals for treatment effects

Achieves asymptotic normality in treatment effect estimates

Enhances heterogeneity detection in treatment effects

Abstract

To further develop the statistical inference problem for heterogeneous treatment effects, this paper builds on Breiman's (2001) random forest tree (RFT)and Wager et al.'s (2018) causal tree to parameterize the nonparametric problem using the excellent statistical properties of classical OLS and the division of local linear intervals based on covariate quantile points, while preserving the random forest trees with the advantages of constructible confidence intervals and asymptotic normality properties [Athey and Imbens (2016),Efron (2014),Wager et al.(2014)\citep{wager2014asymptotic}], we propose a decision tree using quantile classification according to fixed rules combined with polynomial estimation of local samples, which we call the quantile local linear causal tree (QLPRT) and forest (QLPRF).