Penalized GMM Framework for Inference on Functionals of Nonparametric Instrumental Variable Estimators

• URL: http://arxiv.org/abs/2603.29889v2
• Date: Thu, 02 Apr 2026 19:46:57 GMT
• Title: Penalized GMM Framework for Inference on Functionals of Nonparametric Instrumental Variable Estimators
• Abstract summary: This paper develops a penalized GMM framework for automatic debiased inference on functionals of nonparametric instrumental variable estimators.<n>We derive convergence rates for the PGMM estimator and provide conditions for root-n consistency and normality of debiased functional estimates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper develops a penalized GMM (PGMM) framework for automatic debiased inference on functionals of nonparametric instrumental variable estimators. We derive convergence rates for the PGMM estimator and provide conditions for root-n consistency and asymptotic normality of debiased functional estimates, covering both linear and nonlinear functionals. Monte Carlo experiments on average derivative show that the PGMM-based debiased estimator performs on par with the analytical debiased estimator that uses the known closed-form Riesz representer, achieving 90-96% coverage while the plug-in estimator falls below 5%. We apply our procedure to estimate mean own-price elasticities in a semiparametric demand model for differentiated products. Simulations confirm near-nominal coverage while the plug-in severely undercovers. Applied to IRI scanner data on carbonated beverages, debiased semiparametric estimates are approximately 20% more elastic compared to the logit benchmark, and debiasing corrections are heterogeneous across products, ranging from negligible to several times the standard error.

Related papers

• Optimal Nuisance Function Tuning for Estimating a Doubly Robust Functional under Proportional Asymptotics [9.86496801565209]
  We evaluate three existing ECC estimators and two sample splitting strategies for estimating the required nuisance functions.<n>We show that our bias correction strategy yields $sqrtn$-consistent estimators across different sample splitting strategies and estimator choices.<n>Our analysis reveals that prediction- tuning parameters (i.e., those that optimally estimate the nuisance functions) may not lead to the lowest variance of the ECC estimator.
  arXiv  Detail & Related papers  (2025-09-29T21:46:14Z)
• 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)
• Semiparametric conformal prediction [79.6147286161434]
  We construct a conformal prediction set accounting for the joint correlation structure of the vector-valued non-conformity scores.<n>We flexibly estimate the joint cumulative distribution function (CDF) of the scores.<n>Our method yields desired coverage and competitive efficiency on a range of real-world regression problems.
  arXiv  Detail & Related papers  (2024-11-04T14:29:02Z)
• Method-of-Moments Inference for GLMs and Doubly Robust Functionals under Proportional Asymptotics [30.324051162373973]
  We consider the estimation of regression coefficients and signal-to-noise ratio in high-dimensional Generalized Linear Models (GLMs)<n>We derive Consistent and Asymptotically Normal (CAN) estimators of our targets of inference.<n>We complement our theoretical results with numerical experiments and comparisons with existing literature.
  arXiv  Detail & Related papers  (2024-08-12T12:43:30Z)
• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate.<n>We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference [9.940560505044122]
  We propose a method to improve the efficiency and accuracy of amortized Bayesian inference. We estimate the marginal likelihood based on approximate representations of the joint model.
  arXiv  Detail & Related papers  (2023-10-06T17:41:41Z)
• 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)
• Optimization of Annealed Importance Sampling Hyperparameters [77.34726150561087]
  Annealed Importance Sampling (AIS) is a popular algorithm used to estimates the intractable marginal likelihood of deep generative models. We present a parameteric AIS process with flexible intermediary distributions and optimize the bridging distributions to use fewer number of steps for sampling. We assess the performance of our optimized AIS for marginal likelihood estimation of deep generative models and compare it to other estimators.
  arXiv  Detail & Related papers  (2022-09-27T07:58:25Z)
• Support estimation in high-dimensional heteroscedastic mean regression [2.07180164747172]
  We consider a linear mean regression model with random design and potentially heteroscedastic, heavy-tailed errors.<n>We use a strictly convex, smooth variant of the Huber loss function with tuning parameter depending on the parameters of the problem.<n>For the resulting estimator we show sign-consistency and optimal rates of convergence in the $ell_infty$ norm.
  arXiv  Detail & Related papers  (2020-11-03T09:46:31Z)
• SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models [80.22609163316459]
  We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost.
  arXiv  Detail & Related papers  (2020-04-01T11:49:30Z)

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.