Inference on Strongly Identified Functionals of Weakly Identified Functions

• URL: http://arxiv.org/abs/2208.08291v3
• Date: Sat, 1 Jul 2023 01:08:47 GMT
• Title: Inference on Strongly Identified Functionals of Weakly Identified Functions
• Authors: Andrew Bennett, Nathan Kallus, Xiaojie Mao, Whitney Newey, Vasilis Syrgkanis, Masatoshi Uehara
• Abstract summary: We study a novel condition for the functional to be strongly identified even when the nuisance function is not. We propose penalized minimax estimators for both the primary and debiasing nuisance functions.
• Score: 71.42652863687117
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a variety of applications, including nonparametric instrumental variable (NPIV) analysis, proximal causal inference under unmeasured confounding, and 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 function (e.g., NPIV regression) defined by conditional moment restrictions. These nuisance functions are generally weakly identified, in that the conditional moment restrictions can be severely ill-posed as well as admit multiple solutions. This is sometimes resolved by imposing strong conditions that imply the function can be estimated at rates that make inference on the functional possible. In this paper, we study a novel condition for the functional to be strongly identified even when the nuisance function is not; that is, the functional is amenable to asymptotically-normal estimation at $\sqrt{n}$-rates. The condition implies the existence of debiasing nuisance functions, and we propose penalized minimax estimators for both the primary and debiasing nuisance functions. The proposed nuisance estimators can accommodate flexible function classes, and importantly they can converge to fixed limits determined by the penalization regardless of the identifiability of the nuisances. We use the penalized nuisance estimators to form a debiased estimator for the functional of interest and prove its asymptotic normality under generic high-level conditions, which provide for asymptotically valid confidence intervals. We also illustrate our method in a novel partially linear proximal causal inference problem and a partially linear instrumental variable regression problem.

Related papers

• 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)
• Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency [53.90687548731265]
  We study optimal procedures for estimating a linear functional based on observational data. For any convex and symmetric function class $mathcalF$, we derive a non-asymptotic local minimax bound on the mean-squared error.
  arXiv  Detail & Related papers  (2023-01-16T02:57:37Z)
• Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves [4.065100518793487]
  This paper considers general nonlinear sieve quasi-likelihood ratio (GN-QLR) based on expectation inferences of time series data. While the normality of the estimated functionals depends on some unknown Riesz representer of the functional space, we show that the optimally weighted GN-QLR statistic is Chi-square distributed.
  arXiv  Detail & Related papers  (2022-12-31T01:44:17Z)
• Nuisance Function Tuning for Optimal Doubly Robust Estimation [5.018363990542611]
  Estimators of doubly robust functionals typically rely on estimating two complex nuisance functions. We show the interplay between different tuning parameter choices for the nuisance function estimators and sample splitting strategies. Some of these estimators can achieve minimax rates of convergence in all H"older smoothness classes of the nuisance functions.
  arXiv  Detail & Related papers  (2022-12-30T18:17:06Z)
• Sequential Decision Making on Unmatched Data using Bayesian Kernel Embeddings [10.75801980090826]
  We propose a novel algorithm for maximizing the expectation of a function. We take into consideration the uncertainty derived from the estimation of both the conditional distribution of the features and the unknown function. Our algorithm empirically outperforms the current state-of-the-art algorithm in the experiments conducted.
  arXiv  Detail & Related papers  (2022-10-25T01:27:29Z)
• 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)
• Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals [16.768606469968113]
  We consider a class of doubly robust moment functions originally introduced in (Robins et al., 2008) We demonstrate that this moment function can be used to construct estimating equations for the nuisance functions. The convergence rates of the nuisance functions are analyzed using the modern techniques in statistical learning theory.
  arXiv  Detail & Related papers  (2021-04-07T05:52:15Z)
• Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach [84.29777236590674]
  We study the estimation of causal parameters when not all confounders are observed and instead negative controls are available. Recent work has shown how these can enable identification and efficient estimation via two so-called bridge functions.
  arXiv  Detail & Related papers  (2021-03-25T17:59:19Z)

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.