Counterexamples and Sufficient Conditions: Comments on "Optimally-Transported Generalized Method of Moments"
Read the original on arXiv Machine Learning →The paper critiques the optimally‑transported generalized method of moments (OTGMM) estimator introduced by Schennach & Starck (2026a), presenting counterexamples that invalidate Theorems 2–6 under their stated assumptions. It shows that the small‑error assumptions fail to guarantee consistency and asymptotic normality, and that the large‑error analysis leads to a modified‑moment GMM estimator that can diverge from the true OTGMM minimizer, even in simple scalar and overidentified models. The authors further provide a sufficient condition ensuring that solutions of the modified moment equations also solve the original constrained problem, and replace a problematic Assumption 16 with a matrix condition that restores the required bound.
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