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 debiased 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的广义矩方法（GMM）模型中的两步降偏机器学习（DML）估计量，在不依赖交叉拟合的前提下发展了其渐近理论。虽然交叉拟合被广泛使用，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且计算负担沉重。研究表明，通过将尼曼正交矩条件与基于局部化的经验过程方法相结合，可在不进行样本分割的情况下实现有效的统计推断，且允许任意数量的聚类维度。我们证明，在多维聚类依赖条件下，所提出的降偏GMM估计量具有渐近线性和渐近正态性。本文的核心技术贡献在于推导了关于可分可交换阵列之和的一般函数类的全局与局部新极大不等式，这些结论不仅支撑了我们的理论论证，本身也具有独立的研究价值。