This paper develops an asymptotic theory for two-step debiased machine learning (DML) estimators in generalised method of moments (GMM) models with general multiway clustered dependence, without relying on cross-fitting. While cross-fitting is commonly employed, it can be statistically inefficient and computationally burdensome when first-stage learners are complex and the effective sample size is governed by the number of independent clusters. We show that valid inference can be achieved without sample splitting by combining Neyman-orthogonal moment conditions with a localisation-based empirical process approach, allowing for an arbitrary number of clustering dimensions. The resulting DML-GMM estimators are shown to be asymptotically linear and asymptotically normal under multiway clustered dependence. A central technical contribution of the paper is the derivation of novel global and local maximal inequalities for general classes of functions of sums of separately exchangeable arrays, which underpin our theoretical arguments and are of independent interest.

翻译：本文针对具有一般多维聚类依赖关系的广义矩方法（GMM）模型，建立了无需依赖交叉拟合的两步去偏机器学习（DML）估计量的渐近理论。尽管交叉拟合被广泛采用，但当第一阶段学习器较为复杂且有效样本量由独立聚类数量决定时，该方法可能导致统计效率低下并带来沉重的计算负担。我们证明，通过将奈曼正交矩条件与基于局部化的经验过程方法相结合，无需进行样本分割即可实现有效推断，且允许任意维度的聚类结构。所得DML-GMM估计量被证明在多维聚类依赖条件下具有渐近线性与渐近正态性。本文的核心理论贡献在于推导了针对可分离可交换阵列和函数一般类的新型全局与局部极大值不等式，这些不等式构成了我们理论论证的基础，并具有独立的学术价值。