Doubly Robust Inference on Causal Derivative Effects for Continuous Treatments

• URL: http://arxiv.org/abs/2501.06969v1
• Date: Sun, 12 Jan 2025 23:00:16 GMT
• Title: Doubly Robust Inference on Causal Derivative Effects for Continuous Treatments
• Authors: Yikun Zhang, Yen-Chi Chen,
• Abstract summary: We investigate nonparametric inference on the derivative of the dose-response curve with and without the positivity condition. We propose a doubly robust (DR) inference method for estimating the derivative of the dose-response curve using kernel smoothing. In all settings, our DR estimators achieves normality at the standard nonparametric rate of convergence.
• Score: 5.151880096713011
• License:
• Abstract: Statistical methods for causal inference with continuous treatments mainly focus on estimating the mean potential outcome function, commonly known as the dose-response curve. However, it is often not the dose-response curve but its derivative function that signals the treatment effect. In this paper, we investigate nonparametric inference on the derivative of the dose-response curve with and without the positivity condition. Under the positivity and other regularity conditions, we propose a doubly robust (DR) inference method for estimating the derivative of the dose-response curve using kernel smoothing. When the positivity condition is violated, we demonstrate the inconsistency of conventional inverse probability weighting (IPW) and DR estimators, and introduce novel bias-corrected IPW and DR estimators. In all settings, our DR estimator achieves asymptotic normality at the standard nonparametric rate of convergence. Additionally, our approach reveals an interesting connection to nonparametric support and level set estimation problems. Finally, we demonstrate the applicability of our proposed estimators through simulations and a case study of evaluating a job training program.

Related papers

• HNCI: High-Dimensional Network Causal Inference [4.024850952459758]
  We suggest a new method of high-dimensional network causal inference (HNCI) that provides both valid confidence interval on the average direct treatment effect on the treated (ADET) and valid confidence set for the neighborhood size for interference effect.
  arXiv  Detail & Related papers  (2024-12-24T17:41:41Z)
• Semiparametric inference for impulse response functions using double/debiased machine learning [49.1574468325115]
  We introduce a machine learning estimator for the impulse response function (IRF) in settings where a time series of interest is subjected to multiple discrete treatments. The proposed estimator can rely on fully nonparametric relations between treatment and outcome variables, opening up the possibility to use flexible machine learning approaches to estimate IRFs.
  arXiv  Detail & Related papers  (2024-11-15T07:42:02Z)
• Contrastive Balancing Representation Learning for Heterogeneous Dose-Response Curves Estimation [34.20279432270329]
  Estimating the individuals' potential response to varying treatment doses is crucial for decision-making in areas such as precision medicine and management science. We propose a novel Contrastive balancing Representation learning Network using a partial distance measure, called CRNet, for estimating the heterogeneous dose-response curves.
  arXiv  Detail & Related papers  (2024-03-21T08:41:53Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Nonparametric estimation of a covariate-adjusted counterfactual treatment regimen response curve [2.7446241148152253]
  Flexible estimation of the mean outcome under a treatment regimen is a key step toward personalized medicine. We propose an inverse probability weighted nonparametrically efficient estimator of the smoothed regimen-response curve function. Some finite-sample properties are explored with simulations.
  arXiv  Detail & Related papers  (2023-09-28T01:46:24Z)
• Doubly Robust Proximal Causal Learning for Continuous Treatments [56.05592840537398]
  We propose a kernel-based doubly robust causal learning estimator for continuous treatments. We show that its oracle form is a consistent approximation of the influence function. We then provide a comprehensive convergence analysis in terms of the mean square error.
  arXiv  Detail & Related papers  (2023-09-22T12:18:53Z)
• Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency [59.48096489854697]
  The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We prove non-asymptotic upper bounds on the mean-squared error of such procedures. We establish its instance-dependent optimality in finite samples via matching non-asymptotic local minimax lower bounds.
  arXiv  Detail & Related papers  (2022-09-26T23:50:55Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• Near-optimal inference in adaptive linear regression [60.08422051718195]
  Even simple methods like least squares can exhibit non-normal behavior when data is collected in an adaptive manner. We propose a family of online debiasing estimators to correct these distributional anomalies in at least squares estimation. We demonstrate the usefulness of our theory via applications to multi-armed bandit, autoregressive time series estimation, and active learning with exploration.
  arXiv  Detail & Related papers  (2021-07-05T21:05:11Z)
• On the Estimation of Derivatives Using Plug-in Kernel Ridge Regression Estimators [4.392844455327199]
  We propose a simple plug-in kernel ridge regression (KRR) estimator in nonparametric regression. We provide a non-asymotic analysis to study the behavior of the proposed estimator in a unified manner. The proposed estimator achieves the optimal rate of convergence with the same choice of tuning parameter for any order of derivatives.
  arXiv  Detail & Related papers  (2020-06-02T02:32:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.