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Consider the problem of estimating the local average treatment effect with an instrument variable, where the instrument unconfoundedness holds after adjusting for a set of measured covariates. Several unknown functions of the covariates need to be estimated through regression models, such as instrument propensity score and treatment and outcome regression models. We develop a computationally tractable method in high-dimensional settings where the numbers of regression terms are close to or larger than the sample size. Our method exploits regularized calibrated estimation, which involves Lasso penalties but carefully chosen loss functions for estimating coefficient vectors in these regression models, and then employs a doubly robust estimator for the treatment parameter through augmented inverse probability weighting. We provide rigorous theoretical analysis to show that the resulting Wald confidence intervals are valid for the treatment parameter under suitable sparsity conditions if the instrument propensity score model is correctly specified, but the treatment and outcome regression models may be misspecified. For existing high-dimensional methods, valid confidence intervals are obtained for the treatment parameter if all three models are correctly specified. We evaluate the proposed methods via extensive simulation studies and an empirical application to estimate the returns to education.
Covariate-specific treatment effects (CSTEs) represent heterogeneous treatment effects across subpopulations defined by certain selected covariates. In this article, we consider marginal structural models where CSTEs are linearly represented using a
This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions. The method is non-asymptotic in the sense that it provides a finite sample bound on the difference between the tr
We consider the setting in which a strong binary instrument is available for a binary treatment. The traditional LATE approach assumes the monotonicity condition stating that there are no defiers (or compliers). Since this condition is not always obv
Labeling patients in electronic health records with respect to their statuses of having a disease or condition, i.e. case or control statuses, has increasingly relied on prediction models using high-dimensional variables derived from structured and u
Randomization (a.k.a. permutation) inference is typically interpreted as testing Fishers sharp null hypothesis that all effects are exactly zero. This hypothesis is often criticized as uninteresting and implausible. We show, however, that many random