反例与充分条件：对“最优传输广义矩方法”的评论

中文摘要 AI 辅助

我们评论了Schennach & Starck (2026a)提出的最优传输广义矩方法(OTGMM)估计量，并在其所述假设下给出了定理2至定理6的反例。首先，小误差分析中使用的假设不足以支持定理2中的一致性和定理3中的渐近正态性。接下来，我们考虑大误差分析，其中定理4声称OTGMM估计量等价于具有修正矩的GMM估计量。我们证明，在一个标量模型中，定理4选择的值不同于唯一的OTGMM最小化器，并且违反了OTGMM样本矩约束。在满足定理5和定理6所用假设的过度识别模型中，拉格朗日乘子的第一个分量在OTGMM估计量和具有修正矩的GMM估计量下具有不同的概率极限。在误设定下，OTGMM选择的总体值依赖于传输度量以及哪些变量可以被调整。我们给出了一个充分条件，在该条件下，修正矩方程的解在给定参数值处也满足原始约束问题，并给出了OTGMM估计量一致性和渐近正态性的独立条件。我们还证明了假设16并不蕴含补充证明中使用的矩阵界，并用一个能产生该界的矩阵条件替换了假设16。

英文摘要

We comment on the optimally-transported generalized method of moments (OTGMM) estimator proposed by Schennach & Starck (2026a) and give counterexamples to Theorems 2-6 under their stated assumptions. First, the assumptions used in the small-error analysis are insufficient for consistency in Theorem 2 and asymptotic normality in Theorem 3. Next, we consider the large-error analysis, in which Theorem 4 states that the OTGMM estimator is equivalent to a GMM estimator with modified moments. We show that in a scalar model, Theorem 4 selects a value that differs from the unique OTGMM minimizer and violates the OTGMM sample moment restriction. In an overidentified model satisfying the assumptions used in Theorems 5 and 6, the first component of the Lagrange multiplier has different probability limits under the OTGMM estimator and the GMM estimator with modified moments. Under misspecification, the population value selected by OTGMM depends on the transport metric and on which variables may be adjusted. We give a sufficient condition under which solutions of the modified moment equations also solve the original constrained problem at a given parameter value, and separate conditions for consistency and asymptotic normality of the OTGMM estimator. We also show that Assumption 16 does not imply the matrix bound used in the supplemental proofs and replace Assumption 16 with a matrix condition that yields the bound.

发表机构

• The University of Tokyo（东京大学）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

Comment on arXiv:2511.05712