Debiased Inference on Treatment Effect in a High-Dimensional Model

Abstract

This article concerns the potential bias in statistical inference on treatment effects when a large number of covariates are present in a linear or partially linear model. While the estimation bias in an under-fitted model is well understood, we address a lesser-known bias that arises from an over-fitted model. The over-fitting bias can be eliminated through data splitting at the cost of statistical efficiency, and we show that smoothing over random data splits can be pursued to mitigate the efficiency loss. We also discuss some of the existing methods for debiased inference and provide insights into their intrinsic bias-variance trade-off, which leads to an improvement in bias controls. Under appropriate conditions, we show that the proposed estimators for the treatment effects are asymptotically normal and their variances can be well estimated. We discuss the pros and cons of various methods both theoretically and empirically, and show that the proposed methods are valuable options in post-selection inference. Supplementary materials for this article are available online.