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Inference on strongly identified functionals of weakly identified functions

弱识别函数的强识别泛函推断

Abstract In a variety of applications, including nonparametric instrumental variable (NPIV) analysis, proximal causal inference under unmeasured confounding, and analysis of missing-not-at-random data with shadow variables, we are interested in inference on a continuous linear functional (e.g. average causal effects) of nuisance functions (e.g. NPIV regression) defined by conditional moment restrictions. These nuisance functions are often weakly identified, meaning the…

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On the role of surrogates in the efficient estimation of treatment effects with limited outcome data

结果数据有限时替代指标对处理效应高效估计的作用

Abstract In many experimental and observational studies, the outcome of interest is often difficult or expensive to observe, reducing effective sample sizes for estimating average treatment effects (ATEs) even when identifiable. We study how incorporating data on units for which only surrogate outcomes not of primary interest are observed can increase the precision of ATE estimation. We refrain from imposing stringent surrogacy conditions, which permit surrogates as perfect…

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Long-term causal inference under persistent confounding via data combination

持续混杂下通过数据结合开展长期因果推断

Abstract We study the identification and estimation of long-term treatment effects by combining short-term experimental data and long-term observational data subject to unobserved confounding. This problem arises often when concerned with long-term treatment effects since experiments are often short-term due to operational necessity while observational data can be more easily collected over longer time frames but may be subject to confounding. In this paper, we tackle the…

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Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding

未观测混杂下因果推断的双重有效与双重锐性敏感性分析

We consider the problem of constructing bounds on the average treatment effect (ATE) when unmeasured confounders exist but have bounded influence. Specifically, we assume that omitted confounders could not change the odds of treatment for any unit by more than a fixed factor. We derive the sharp partial identification bounds implied by this assumption by leveraging distributionally robust optimization, and we propose estimators of these bounds with several novel robustness…

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Efficient evaluation of natural stochastic policies in off-line reinforcement learning

离线强化学习中自然随机策略的有效评估

Summary We study the efficient off-policy evaluation of natural stochastic policies, which are defined in terms of deviations from the unknown behaviour policy. This is a departure from the literature on off-policy evaluation that largely considers the evaluation of explicitly specified policies. Crucially, off-line reinforcement learning with natural stochastic policies can help alleviate issues of weak overlap, lead to policies that build upon current practice and improve…

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The variational method of moments

变分矩方法

Abstract The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. We introduce a very general class of estimators called the variational method of moments (VMM), motivated by a variational minimax reformulation of optimally weighted generalized method of moments for finite sets of moments. VMM controls infinitely for many moments characterized by…

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More Efficient Policy Learning via Optimal Retargeting

通过最优目标人群重设提高策略学习效率

Nathan Kallus* School of Operations Research and Information Engineering and Cornell Tech, Cornell University, New York, NYColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA.Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.CONTACT Nathan Kallus kallus@cornell.edu School of Operations Research and Information Engineering and Cornell Tech, Cornell University, 2 West…

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On the Optimality of Randomization in Experimental Design: How to Randomize for Minimax Variance and Design-Based Inference

实验设计中随机化的最优性:极小极大方差与基于设计的推断

Abstract I study the minimax-optimal design for a two-arm controlled experiment where conditional mean outcomes vary in a given set and the objective is effect-estimation precision. When this set is permutation symmetric, the optimal design is shown to be complete randomization. Notably, even when the set has structure (i.e., is not permutation symmetric), being minimax-optimal for precision still requires randomization beyond a single partition of units, that is, beyond…

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Optimal A Priori Balance in the Design of Controlled Experiments

受控实验设计中的最优事前平衡

Summary We develop a unified theory of designs for controlled experiments that balance baseline covariates a priori (before treatment and before randomization) using the framework of minimax variance and a new method called kernel allocation. We show that any notion of a priori balance must go hand in hand with a notion of structure, since with no structure on the dependence of outcomes on baseline covariates complete randomization (no special covariate balance) is always…

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