mlsanityData to 13 Oct 2026

Kernel Conditional Moment Test via Maximum Moment Restriction

arXiv 2002.09225 ↗First posted 21 Feb 2020math.ST cs.LG econ.EMcited by 18

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Abstract (arXiv)

We propose a new family of specification tests called kernel conditional moment (KCM) tests. Our tests are built on a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS) called conditional moment embedding (CMME). After transforming the conditional moment restrictions into a continuum of unconditional counterparts, the test statistic is defined as the maximum moment restriction (MMR) within the unit ball of the RKHS. We show that the MMR not only fully characterizes the original conditional moment restrictions, leading to consistency in both hypothesis testing and parameter estimation, but also has an analytic expression that is easy to compute as well as closed-form asymptotic distributions. Our empirical studies show that the KCM test has a promising finite-sample performance compared to existing tests.

Key facts. Cited by 18 papers in the map (data through 13 Oct 2026). First posted on arXiv 21 Feb 2020.

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Citing papers per year: 2021: 2; 2022: 4; 2023: 7; 2024: 1; 2025: 3; 2026: 1.

18 papers.

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  1. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 55
  2. 2023Identifying Representations for Intervention Extrapolationcited by 21
  3. 2023Demystifying Causal Features on Adversarial Examples and Causal Inoculation for Robust Network by Adversarial Instrumental Variable Regressioncited by 18
  4. 2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 14
  5. 2022Spectral Representation Learning for Conditional Moment Modelscited by 12
  6. 2023Falsification of Internal and External Validity in Observational Studies via Conditional Moment Restrictionscited by 10
  7. 2022Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictionscited by 8
  8. 2023Estimation Beyond Data Reweighting: Kernel Method of Momentscited by 5
  9. 2023Doubly Robust Proximal Causal Learning for Continuous Treatmentscited by 4
  10. 2024Benchmarking Observational Studies with Experimental Data under Right-Censoringcited by 4
  11. 2025The Hardness of Validating Observational Studies with Experimental Datacited by 4
  12. 2021Instrument Space Selection for Kernel Maximum Moment Restrictioncited by 2
6 more
  1. 2022Correcting Confounding via Random Selection of Background Variablescited by 2
  2. 2023Kernel Conditional Moment Constraints for Confounding Robust Inferencecited by 2
  3. 2025Density Ratio-Free Doubly Robust Proxy Causal Learningcited by 1
  4. 2023A Convex Framework for Confounding Robust Inferencecited by 0
  5. 2025Learning Treatment Representations for Downstream Instrumental Variable Regressioncited by 0
  6. 2026Same Flow, Different Paths: Variance Reduction in Flow Matchingcited by 0